Optional sensor calibration in continuous glucose monitoring

ABSTRACT

A method for optional external calibration of a calibration-free glucose sensor uses values of measured working electrode current (Isig) and EIS data to calculate a final sensor glucose (SG) value. Counter electrode voltage (Vcntr) may also be used as an input. Raw Isig and Vcntr values may be preprocessed, and low-pass filtering, averaging, and/or feature generation may be applied. SG values may be generated using one or more models for predicting SG calculations. When an external blood glucose (BG) value is available, the BG value may also be used in calculating the SG values. A SG variance estimate may be calculated for each predicted SG value and modulated, with the modulated SG values then fused to generate a fused SG. A Kalman filter, as well as error detection logic, may be applied to the fused SG value to obtain a final SG, which is then displayed to the user.

FIELD OF THE INVENTION

Embodiments of this invention are related generally to subcutaneous andimplantable sensor devices and, in particular embodiments, to optionalcalibration in calibration-free systems, devices, and methods.

BACKGROUND OF THE INVENTION

Subjects (e.g., patients) and medical personnel wish to monitor readingsof physiological conditions within the subject's body. Illustratively,subjects wish to monitor blood glucose levels in a subject's body on acontinuing basis. Presently, a patient can measure his/her blood glucose(BG) using a BG measurement device (i.e. glucose meter), such as a teststrip meter, a continuous glucose measurement system (or a continuousglucose monitor), or a hospital hemacue. BG measurement devices usevarious methods to measure the BG level of a patient, such as a sampleof the patient's blood, a sensor in contact with a bodily fluid, anoptical sensor, an enzymatic sensor, or a fluorescent/fluorescentquenching sensor. When the BG measurement device has generated a BGmeasurement, the measurement is displayed on the BG measurement device.

Infusion pump devices and systems are relatively well known in themedical arts for use in delivering or dispensing a prescribedmedication, such as insulin, to a patient. In one form, such devicescomprise a relatively compact pump housing adapted to receive a syringeor reservoir carrying a prescribed medication for administration to thepatient through infusion tubing and an associated catheter or infusionset. Programmable controls can operate the infusion pump continuously orat periodic intervals to obtain a closely controlled and accuratedelivery of the medication over an extended period of time. Suchinfusion pumps are used to administer insulin and other medications,with exemplary pump constructions being shown and described in U.S. Pat.Nos. 4,562,751; 4,678,408; 4,685,903; 5,080,653; and 5,097,122, whichare incorporated by reference herein.

There is a baseline insulin need for each body which, in diabeticindividuals, may generally be maintained by administration of a basalamount of insulin to the patient on a continual, or continuous, basisusing infusion pumps. However, when additional glucose (i.e., beyond thebasal level) appears in a diabetic individual's body, such as, forexample, when the individual consumes a meal, the amount and timing ofthe insulin to be administered must be determined so as to adequatelyaccount for the additional glucose while, at the same time, avoidinginfusion of too much insulin. Typically, a bolus amount of insulin isadministered to compensate for meals (i.e., meal bolus). It is commonfor diabetics to determine the amount of insulin that they may need tocover an anticipated meal based on the carbohydrate content of the meal.

Over the years, a variety of electrochemical glucose sensors have beendeveloped for use in obtaining an indication of blood glucose levels ina diabetic patient. Such readings are useful in monitoring and/oradjusting a treatment regimen which typically includes the regularadministration of insulin to the patient. Generally, small and flexibleelectrochemical sensors can be used to obtain periodic readings over anextended period of time. In one form, flexible subcutaneous sensors areconstructed in accordance with thin film mask techniques. Typical thinfilm sensors are described in commonly-assigned U.S. Pat. Nos.5,390,671; 5,391,250; 5,482,473; and 5,586,553 which are incorporated byreference herein.

These electrochemical sensors have been applied in a telemeteredcharacteristic monitor system. As described, e.g., in commonly-assignedU.S. Pat. No. 6,809,653 (“the '653 patent”), the entire contents ofwhich are incorporated herein by reference, the telemetered systemincludes a remotely located data receiving device, a sensor forproducing signals indicative of a characteristic of a user, and atransmitter device for processing signals received from the sensor andfor wirelessly transmitting the processed signals to the remotelylocated data receiving device. The data receiving device may be acharacteristic monitor, a data receiver that provides data to anotherdevice, an RF programmer, a medication delivery device (such as aninfusion pump), or the like.

Current continuous glucose measurement systems include subcutaneous (orshort-term) sensors and implantable (or long-term) sensors. For each ofthe short-term sensors and the long-term sensors, a patient has to waita certain amount of time in order for the continuous glucose sensor tostabilize and to provide accurate readings. In many continuous glucosesensors, the subject must wait three hours for the continuous glucosesensor to stabilize before any glucose measurements are utilized. Thisis an inconvenience for the patient and in some cases may cause thepatient not to utilize a continuous glucose measurement system.

Further, when a glucose sensor is first inserted into a patient's skinor subcutaneous layer, the glucose sensor does not operate in a stablestate. The electrical readings from the sensor, which represent theglucose level of the patient, vary over a wide range of readings. In thepast, sensor stabilization used to take several hours. A technique forsensor stabilization is detailed, e.g., in the '653 patent, where theinitialization process for sensor stabilization may be reduced toapproximately one hour. A high voltage (e.g., 1.0-1.2 volts) may beapplied for 1 to 2 minutes to allow the sensor to stabilize and then alow voltage (e.g., between 0.5-0.6 volts) may be applied for theremainder of the initialization process (e.g., 58 minutes or so).

It is also desirable to allow electrodes of the sensor to besufficiently “wetted” or hydrated before utilization of the electrodesof the sensor. If the electrodes of the sensor are not sufficientlyhydrated, the result may be inaccurate readings of the patient'sphysiological condition. A user of current blood glucose sensors may beinstructed to not power up the sensors immediately. If they are utilizedtoo early, such blood glucose sensors may not operate in an optimal orefficient fashion.

Much of the existing state of the art in continuous glucose monitoring(CGM) is largely adjunctive, meaning that the readings provided by a CGMdevice (including, e.g., an implantable or subcutaneous sensor) cannotbe used without a reference value in order to make a clinical decision.The reference value, in turn, must be obtained from a finger stickusing, e.g., a BG meter. The reference value is needed because there isa limited amount of information that is available from thesensor/sensing component. Specifically, only the raw sensor value (i.e.,the sensor current or Isig) and the counter voltage may be provided bythe sensing component for processing. Therefore, during analysis, if itappears that the raw sensor signal is abnormal (e.g., if the signal isdecreasing), the only way one can distinguish between a sensor failureand a physiological change within the user/patient (i.e., glucose levelchanging in the body) may be by acquiring a reference glucose value viaa finger stick. As is known, the reference finger stick is also used forcalibrating the sensor.

The art has searched for ways to eliminate or, at the very least,minimize, the number of finger sticks that are necessary for calibrationand for assessing sensor health. However, given the number and level ofcomplexity of the multitude of sensor failure modes, no satisfactorysolution has been found. At most, diagnostics have been developed thatare based on either direct assessment of the Isig, or on comparison oftwo Isigs. In either case, because the Isig tracks the level of glucosein the body, by definition, it is not analyte independent. As such, byitself, the Isig is not a reliable source of information for sensordiagnostics, nor is it a reliable predictor for continued sensorperformance.

Another limitation that has existed in the art thus far has been thelack of sensor electronics that can not only run the sensor, but alsoperform real-time sensor and electrode diagnostics, and do so forredundant electrodes, redundant sensors, complementary sensors, andredundant and complementary sensors, all while managing the sensor'spower supply. To be sure, the concept of electrode redundancy has beenaround for quite some time. However, in the past, there has been littleto no success in using electrode redundancy (and/or complementary andredundant electrodes) not only for obtaining more than one reading at atime, but also for assessing the relative health of the redundantelectrodes, the overall reliability of the sensor, and the frequency ofthe need, if at all, for calibration reference values.

In addition, even when redundant sensing electrodes have been used, thenumber has typically been limited to two. Again, this has been duepartially to the absence of advanced electronics that run, assess, andmanage a multiplicity of independent working electrodes (e.g., up to 5or more) in real time. Another reason, however, has been the limitedview that redundant electrodes are used in order to obtain “independent”sensor signals and, for that purpose, two redundant electrodes aresufficient. As noted, while this is one function of utilizing redundantelectrodes, it is not the only one.

SUMMARY

According to embodiments of the invention, a method for optionalexternal calibration of a calibration-free glucose sensor for measuringthe level of glucose in a body of a user, wherein the glucose sensorincludes physical sensor electronics, a microcontroller, and a workingelectrode, comprises: periodically measuring, by the physical sensorelectronics, electrode current (Isig) signals for the working electrode;performing, by the microcontroller, an Electrochemical ImpedanceSpectroscopy (EIS) procedure to generate EIS-related data for theworking electrode; based on the Isig signals and EIS-related data and aplurality of calibration-free SG-predictive models, calculating, by themicrocontroller, a respective sensor glucose (SG) value for each of theSG-predictive models; calculating, by the microcontroller, a SG varianceestimate for each respective SG value; determining, by themicrocontroller, whether an external blood glucose (BG) value isavailable and, when available, incorporating the BG value into thecalculation of the SG value; fusing, by the microcontroller, therespective SG values from the plurality of SG-predictive models toobtain a single, fused SG value; applying, by the microcontroller, anunscented Kalman filter to the fused SG value; and calculating, by themicrocontroller, a calibrated SG value to be displayed to the user.

BRIEF DESCRIPTION OF THE DRAWINGS

A detailed description of embodiments of the invention will be made withreference to the accompanying drawings, wherein like numerals designatecorresponding parts in the figures.

FIG. 1 is a perspective view of a subcutaneous sensor insertion set andblock diagram of a sensor electronics device according to an embodimentof the invention.

FIG. 2A illustrates a substrate having two sides, a first side whichcontains an electrode configuration and a second side which containselectronic circuitry.

FIG. 2B illustrates a general block diagram of an electronic circuit forsensing an output of a sensor.

FIG. 3 illustrates a block diagram of a sensor electronics device and asensor including a plurality of electrodes according to an embodiment ofthe invention.

FIG. 4 illustrates an alternative embodiment of the invention includinga sensor and a sensor electronics device according to an embodiment ofthe invention.

FIG. 5 illustrates an electronic block diagram of the sensor electrodesand a voltage being applied to the sensor electrodes according to anembodiment of the invention.

FIG. 6A illustrates a method of applying pulses during a stabilizationtimeframe in order to reduce the stabilization timeframe according to anembodiment of the invention.

FIG. 6B illustrates a method of stabilizing sensors according to anembodiment of the invention.

FIG. 6C illustrates utilization of feedback in stabilizing the sensorsaccording to an embodiment of the invention.

FIG. 7 illustrates an effect of stabilizing a sensor according to anembodiment of the invention.

FIG. 8A illustrates a block diagram of a sensor electronics device and asensor including a voltage generation device according to an embodimentof the invention.

FIG. 8B illustrates a voltage generation device to implement thisembodiment of the invention.

FIG. 8C illustrates a voltage generation device to generate two voltagevalues according to an embodiment of the invention.

FIG. 8D illustrates a voltage generation device having three voltagegeneration systems, according to embodiments of the invention.

FIG. 9A illustrates a sensor electronics device including amicrocontroller for generating voltage pulses according to an embodimentof the invention.

FIG. 9B illustrates a sensor electronics device including an analyzationmodule according to an embodiment of the invention.

FIG. 10 illustrates a block diagram of a sensor system includinghydration electronics according to an embodiment of the invention.

FIG. 11 illustrates an embodiment of the invention including amechanical switch to assist in determining a hydration time.

FIG. 12 illustrates a method of detection of hydration according to anembodiment of the invention.

FIG. 13A illustrates a method of hydrating a sensor according to anembodiment of the present invention.

FIG. 13B illustrates an additional method for verifying hydration of asensor according to an embodiment of the invention.

FIGS. 14A, 14B, and 14C illustrate methods of combining hydrating of asensor with stabilizing a sensor according to an embodiment of theinvention.

FIG. 15A illustrates EIS-based analysis of system response to theapplication of a periodic AC signal in accordance with embodiments ofthe invention.

FIG. 15B illustrates a known circuit model for electrochemical impedancespectroscopy.

FIG. 16A illustrates an example of a Nyquist plot where, for a selectedfrequency spectrum from 0.1 Hz to 1000 Mhz, AC voltages plus a DCvoltage (DC bias) are applied to the working electrode in accordancewith embodiments of the invention.

FIG. 16B shows another example of a Nyquist plot with a linear fit forthe relatively-lower frequencies and the intercept approximating thevalue of real impedance at the relatively-higher frequencies.

FIGS. 16C and 16D show, respectively, infinite and finite glucose sensorresponse to a sinusoidal working potential.

FIG. 16E shows a Bode plot for magnitude in accordance with embodimentsof the invention.

FIG. 16F shows a Bode plot for phase in accordance with embodiments ofthe invention.

FIG. 17 illustrates the changing Nyquist plot of sensor impedance as thesensor ages in accordance with embodiments of the invention.

FIG. 18 illustrates methods of applying EIS technique in stabilizing anddetecting the age of the sensor in accordance with embodiments of theinvention.

FIG. 19 illustrates a schedule for performing the EIS procedure inaccordance with embodiments of the invention.

FIG. 20 illustrates a method of detecting and repairing a sensor usingEIS procedures in conjunction with remedial action in accordance withembodiments of the invention.

FIGS. 21A and 21B illustrate examples of a sensor remedial action inaccordance with embodiments of the invention.

FIG. 22 shows a Nyquist plot for a normally-functioning sensor where theNyquist slope gradually increases, and the intercept graduallydecreases, as the sensor wear-time progresses.

FIG. 23A shows raw current signal (Isig) from two redundant workingelectrodes, and the electrodes' respective real impedances at 1 kHz, inaccordance with embodiments of the invention.

FIG. 23B shows the Nyquist plot for the first working electrode (WE1) ofFIG. 23A.

FIG. 23C shows the Nyquist plot for the second working electrode (WE2)of FIG. 23A.

FIG. 24 illustrates examples of signal dip for two redundant workingelectrodes, and the electrodes' respective real impedances at 1 kHz, inaccordance with embodiments of the invention.

FIG. 25A illustrates substantial glucose independence of real impedance,imaginary impedance, and phase at relatively-higher frequencies for anormally-functioning glucose sensor in accordance with embodiments ofthe invention.

FIG. 25B shows illustrative examples of varying levels of glucosedependence of real impedance at the relatively-lower frequencies inaccordance with embodiments of the invention.

FIG. 25C shows illustrative examples of varying levels of glucosedependence of phase at the relatively-lower frequencies in accordancewith embodiments of the invention.

FIG. 26 shows the trending for 1 kHz real impedance, 1 kHz imaginaryimpedance, and relatively-higher frequency phase as a glucose sensorloses sensitivity as a result of oxygen deficiency at the sensorinsertion site, according to embodiments of the invention.

FIG. 27 shows Isig and phase for an in-vitro simulation of oxygendeficit at different glucose concentrations in accordance withembodiments of the invention.

FIGS. 28A-28C show an example of oxygen deficiency-led sensitivity losswith redundant working electrodes WE1 and WE2, as well as theelectrodes' EIS-based parameters, in accordance with embodiments of theinvention.

FIG. 28D shows EIS-induced spikes in the raw Isig for the example ofFIGS. 28A-28C.

FIG. 29 shows an example of sensitivity loss due to oxygen deficiencythat is caused by an occlusion, in accordance with embodiments of theinvention.

FIGS. 30A-30C show an example of sensitivity loss due to bio-fouling,with redundant working electrodes WE1 and WE2, as well as theelectrodes' EIS-based parameters, in accordance with embodiments of theinvention.

FIG. 30D shows EIS-induced spikes in the raw Isig for the example ofFIGS. 30A-30C.

FIG. 31 shows a diagnostic procedure for sensor fault detection inaccordance with embodiments of the invention.

FIGS. 32A and 32B show another diagnostic procedure for sensor faultdetection in accordance with embodiments of the invention.

FIG. 33A shows a top-level flowchart involving a current (Isig)-basedfusion algorithm in accordance with embodiments of the invention.

FIG. 33B shows a top-level flowchart involving a sensor glucose(SG)-based fusion algorithm in accordance with embodiments of theinvention.

FIG. 34 shows details of the sensor glucose (SG)-based fusion algorithmof FIG. 33B in accordance with embodiments of the invention.

FIG. 35 shows details of the current (Isig)-based fusion algorithm ofFIG. 33A in accordance with embodiments of the invention.

FIG. 36 is an illustration of calibration for a sensor in steady state,in accordance with embodiments of the invention.

FIG. 37 is an illustration of calibration for a sensor in transition, inaccordance with embodiments of the invention.

FIG. 38A is an illustration of EIS-based dynamic slope (with slopeadjustment) in accordance with embodiments of the invention for sensorcalibration.

FIG. 38B shows an EIS-assisted sensor calibration flowchart involvinglow start-up detection in accordance with embodiments of the invention.

FIG. 39 shows sensor current (Isig) and 1 kHz impedance magnitude for anin-vitro simulation of an interferent being in close proximity to asensor in accordance with embodiments of the invention.

FIGS. 40A and 40B show Bode plots for phase and impedance, respectively,for the simulation shown in FIG. 39.

FIG. 40C shows a Nyquist plot for the simulation shown in FIG. 39.

FIG. 41 shows another in-vitro simulation with an interferent inaccordance to embodiments of the invention.

FIGS. 42A and 42B illustrate an ASIC block diagram in accordance withembodiments of the invention.

FIG. 43 shows a potentiostat configuration for a sensor with redundantworking electrodes in accordance with embodiments of the invention.

FIG. 44 shows an equivalent AC inter-electrode circuit for a sensor withthe potentiostat configuration shown in FIG. 43.

FIG. 45 shows some of the main blocks of the EIS circuitry in the analogfront end IC of a glucose sensor in accordance with embodiments of theinvention.

FIGS. 46A-46F show a simulation of the signals of the EIS circuitryshown in FIG. 45 for a current of 0-degree phase with a 0-degree phasemultiply.

FIGS. 47A-47F show a simulation of the signals of the EIS circuitryshown in FIG. 45 for a current of 0-degree phase with a 90-degree phasemultiply.

FIG. 48 shows a circuit model in accordance with embodiments of theinvention.

FIGS. 49A-49C show illustrations of circuit models in accordance withalternative embodiments of the invention.

FIG. 50A is a Nyquist plot overlaying an equivalent circuit simulationin accordance with embodiments of the invention.

FIG. 50B is an enlarged diagram of the high-frequency portion of FIG.50A.

FIG. 51 shows a Nyquist plot with increasing Cdl in the direction ofArrow A, in accordance with embodiments of the invention.

FIG. 52 shows a Nyquist plot with increasing α in the direction of ArrowA, in accordance with embodiments of the invention.

FIG. 53 shows a Nyquist plot with increasing Rp in the direction ofArrow A, in accordance with embodiments of the invention.

FIG. 54 shows a Nyquist plot with increasing Warburg admittance in thedirection of Arrow A, in accordance with embodiments of the invention.

FIG. 55 shows a Nyquist plot with increasing λ in the direction of ArrowA, in accordance with embodiments of the invention.

FIG. 56 shows the effect of membrane capacitance on the Nyquist plot, inaccordance with embodiments of the invention.

FIG. 57 shows a Nyquist plot with increasing membrane resistance in thedirection of Arrow A, in accordance with embodiments of the invention.

FIG. 58 shows a Nyquist plot with increasing Rsol in the direction ofArrow A, in accordance with embodiments of the invention.

FIGS. 59A-59C show changes in EIS parameters relating to circuitelements during start-up and calibration in accordance with embodimentsof the invention.

FIGS. 60A-60C show changes in a different set of EIS parameters relatingto circuit elements during start-up and calibration in accordance withembodiments of the invention.

FIGS. 61A-61C show changes in yet a different set of EIS parametersrelating to circuit elements during start-up and calibration inaccordance with embodiments of the invention.

FIG. 62 shows the EIS response for multiple electrodes in accordancewith embodiments of the invention.

FIG. 63 is a Nyquist plot showing the effect of Isig calibration via anincrease in glucose in accordance with embodiments of the invention.

FIG. 64 shows the effect of oxygen (Vcntr) response on the Nyquist plot,in accordance with embodiments of the invention.

FIG. 65 shows a shift in the Nyquist plot due to temperature changes, inaccordance with embodiments of the invention.

FIG. 66 shows the relationship between Isig and blood glucose inaccordance with embodiments of the invention.

FIGS. 67A-67B show sensor drift in accordance with embodiments of theinvention.

FIG. 68 shows an increase in membrane resistance during sensitivityloss, in accordance with embodiments of the invention.

FIG. 69 shows a drop in Warburg Admittance during sensitivity loss, inaccordance with embodiments of the invention.

FIG. 70 shows calibration curves in accordance with embodiments of theinvention.

FIG. 71 shows a higher-frequency semicircle becoming visible on aNyquist plot in accordance with embodiments of the invention.

FIGS. 72A and 72B show Vcntr rail and Cdl decrease in accordance withembodiments of the invention.

FIG. 73 shows the changing slope of calibration curves in accordancewith embodiments of the invention

FIG. 74 shows the changing length of the Nyquist plot in accordance withembodiments of the invention.

FIG. 75 shows enlarged views of the lower-frequency and thehigher-frequency regions of the Nyquist plot of FIG. 74.

FIGS. 76A and 76B show the combined effect of increase in membraneresistance, decrease in Cdl, and Vcntr rail in accordance withembodiments of the invention.

FIG. 77 shows relative Cdl values for two working electrodes inaccordance with embodiments of the invention.

FIG. 78 shows relative Rp values for two working electrodes inaccordance with embodiments of the invention.

FIG. 79 shows the combined effect of changing EIS parameters oncalibration curves in accordance with embodiments of the invention.

FIG. 80 shows that, in accordance with embodiments of the invention, thelength of the Nyquist plot in the lower-frequency region is longer wherethere is sensitivity loss.

FIG. 81 is a flow diagram for sensor self-calibration based on thedetection of sensitivity change in accordance with embodiments of theinvention.

FIG. 82 illustrates a horizontal shift in Nyquist plot as a result ofsensitivity loss, in accordance with embodiments of the invention.

FIG. 83 shows a method of developing a heuristic EIS metric based on aNyquist plot in accordance with embodiments of the invention.

FIG. 84 shows the relationship between Rm and Calibration Factor inaccordance with embodiments of the invention.

FIG. 85 shows the relationship between Rm and normalized Isig inaccordance with embodiments of the invention.

FIG. 86 shows Isig plots for various glucose levels as a function oftime, in accordance with embodiments of the invention.

FIG. 87 shows Cdl plots for various glucose levels as a function oftime, in accordance with embodiments of the invention.

FIG. 88 shows a second inflection point for the plots of FIG. 86, inaccordance with embodiments of the invention.

FIG. 89 shows a second inflection point for Rm corresponding to the peakin FIG. 88, in accordance with embodiments of the invention.

FIG. 90 shows one illustration of the relationship between CalibrationFactor (CF) and Rmem+Rsol in accordance with embodiments of theinvention.

FIG. 91A is a chart showing in-vivo results for MARD over all valid BGsin approximately the first 8 hours of sensor life, in accordance withembodiments of the invention.

FIG. 91B is a chart showing median ARD numbers over all valid BGs inapproximately the first 8 hours of sensor life, in accordance withembodiments of the invention.

FIGS. 92A-92C show Calibration Factor adjustment in accordance withembodiments of the invention.

FIGS. 93A-93C show Calibration Factor adjustment in accordance withembodiments of the invention.

FIGS. 94A-94C show Calibration Factor adjustment in accordance withembodiments of the invention.

FIG. 95 shows an illustrative example of initial decay in Cdl inaccordance with embodiments of the invention.

FIG. 96 shows the effects on Isig of removal of the non-Faradaiccurrent, in accordance with embodiments of the invention.

FIG. 97A shows the Calibration Factor before removal of the non-Faradaiccurrent for two working electrodes, in accordance with embodiments ofthe invention.

FIG. 97B shows the Calibration Factor after removal of the non-Faradaiccurrent for two working electrodes, in accordance with embodiments ofthe invention.

FIGS. 98A and 98B show the effect on MARD of the removal of thenon-Faradaic current, in accordance with embodiments of the invention.

FIG. 99 is an illustration of double layer capacitance over time, inaccordance with embodiments of the invention.

FIG. 100 shows a shift in Rmem+Rsol and the appearance of thehigher-frequency semicircle during sensitivity loss, in accordance withembodiments of the invention.

FIG. 101A shows a flow diagram for detection of sensitivity loss usingcombinatory logic, in accordance with an embodiment of the invention.

FIG. 101B shows a flow diagram for detection of sensitivity loss usingcombinatory logic, in accordance with another embodiment of theinvention.

FIG. 102 shows an illustrative method for using Nyquist slope as amarker to differentiate between new and used sensors, in accordance withembodiments of the invention.

FIGS. 103A-103C show an illustrative example of Nyquist plots havingdifferent lengths for different sensor configurations, in accordancewith embodiments of the invention.

FIG. 104 shows Nyquist plot length as a function of time, for thesensors of FIGS. 103A-103C.

FIG. 105 shows a flow diagram for blanking sensor data or terminating asensor in accordance with an embodiment of the invention.

FIG. 106 shows a flow diagram for sensor termination in accordance withan embodiment of the invention.

FIG. 107 shows a flow diagram for signal dip detection in accordancewith an embodiment of the invention.

FIG. 108A shows Isig and Vcntr as a function of time, and FIG. 108Bshows glucose as a function of time, in accordance with an embodiment ofthe invention.

FIG. 109A calibration ratio as a function of time, and FIG. 109B showglucose as a function of time, in accordance with an embodiment of theinvention.

FIGS. 110A and 110B show calibration factor trends as a function of timein accordance with embodiments of the invention.

FIG. 111 shows a flow diagram for First Day Calibration (FDC) inaccordance with an embodiment of the invention.

FIG. 112 shows a flow diagram for EIS-based calibration in accordancewith an embodiment of the invention.

FIG. 113 shows a flow diagram for an existing calibration methodology.

FIG. 114 shows a calibration flow diagram in accordance with embodimentsof the invention.

FIG. 115 shows a calibration flow diagram in accordance with otherembodiments of the invention.

FIG. 116 shows a calibration flow diagram in accordance with yet otherembodiments of the invention.

FIG. 117 shows a calibration flow diagram in accordance with otherembodiments of the invention.

FIG. 118 shows a table of comparative MARD values calculated based onembodiments of the invention.

FIG. 119 shows a flow diagram for calculation of raw fusion weights inaccordance with embodiments of the invention.

FIG. 120 shows a Sensor Glucose (SG) fusion logic diagram in accordancewith embodiments of the invention.

FIG. 121 shows a flow diagram of a calibration-free retrospectivealgorithm in accordance with an embodiment of the invention.

FIG. 122 shows a decision tree model in accordance with embodiments ofthe invention.

FIG. 123 shows a decision tree model for blanking data in accordancewith an embodiment of the invention.

FIG. 124 is a table showing examples of parameters for a blankingalgorithm in accordance with embodiments of the invention.

FIG. 125 shows fusion, filtering, and blanking results in accordancewith embodiments of the invention.

FIG. 126 shows a flow diagram of an optional calibration logic inaccordance with embodiments of the invention.

FIG. 127 shows a table of comparison between two different glucosesensor designs.

FIG. 128 shows an example of complex redundancy in accordance withembodiments of the invention.

FIG. 129 shows a block diagram including a calibrated model and anon-calibrated model in accordance with embodiments of the invention.

FIG. 130 shows a diagram of fusion logic in accordance with embodimentsof the invention.

FIG. 131 shows a diagram for fusion logic with one calibrated model andone non-calibrated model in accordance with embodiments of theinvention.

FIG. 132 shows a diagram for fusion logic with two non-calibrated modelsin accordance with embodiments of the invention.

FIG. 133 shows a diagram for fusion logic with two calibrated models inaccordance with embodiments of the invention.

FIG. 134 shows a diagram for fusion logic with multiple calibratedmodels and/or multiple non-calibrated models in accordance withembodiments of the invention.

DETAILED DESCRIPTION

In the following description, reference is made to the accompanyingdrawings which form a part hereof and which illustrate severalembodiments of the present inventions. It is understood that otherembodiments may be utilized and structural and operational changes maybe made without departing from the scope of the present inventions.

The inventions herein are described below with reference to flowchartillustrations of methods, systems, devices, apparatus, and programmingand computer program products. It will be understood that each block ofthe flowchart illustrations, and combinations of blocks in the flowchartillustrations, can be implemented by programming instructions, includingcomputer program instructions (as can any menu screens described in thefigures). These computer program instructions may be loaded onto acomputer or other programmable data processing apparatus (such as acontroller, microcontroller, or processor in a sensor electronicsdevice) to produce a machine, such that the instructions which executeon the computer or other programmable data processing apparatus createinstructions for implementing the functions specified in the flowchartblock or blocks. These computer program instructions may also be storedin a computer-readable memory that can direct a computer or otherprogrammable data processing apparatus to function in a particularmanner, such that the instructions stored in the computer-readablememory produce an article of manufacture including instructions whichimplement the function specified in the flowchart block or blocks. Thecomputer program instructions may also be loaded onto a computer orother programmable data processing apparatus to cause a series ofoperational steps to be performed on the computer or other programmableapparatus to produce a computer implemented process such that theinstructions which execute on the computer or other programmableapparatus provide steps for implementing the functions specified in theflowchart block or blocks, and/or menus presented herein. Programminginstructions may also be stored in and/or implemented via electroniccircuitry, including integrated circuits (ICs) and Application SpecificIntegrated Circuits (ASICs) used in conjunction with sensor devices,apparatuses, and systems.

FIG. 1 is a perspective view of a subcutaneous sensor insertion set anda block diagram of a sensor electronics device according to anembodiment of the invention. As illustrated in FIG. 1, a subcutaneoussensor set 10 is provided for subcutaneous placement of an activeportion of a flexible sensor 12 (see, e.g., FIG. 2), or the like, at aselected site in the body of a user. The subcutaneous or percutaneousportion of the sensor set 10 includes a hollow, slotted insertion needle14, and a cannula 16. The needle 14 is used to facilitate quick and easysubcutaneous placement of the cannula 16 at the subcutaneous insertionsite. Inside the cannula 16 is a sensing portion 18 of the sensor 12 toexpose one or more sensor electrodes 20 to the user's bodily fluidsthrough a window 22 formed in the cannula 16. In an embodiment of theinvention, the one or more sensor electrodes 20 may include a counterelectrode, a reference electrode, and one or more working electrodes.After insertion, the insertion needle 14 is withdrawn to leave thecannula 16 with the sensing portion 18 and the sensor electrodes 20 inplace at the selected insertion site.

In particular embodiments, the subcutaneous sensor set 10 facilitatesaccurate placement of a flexible thin film electrochemical sensor 12 ofthe type used for monitoring specific blood parameters representative ofa user's condition. The sensor 12 monitors glucose levels in the body,and may be used in conjunction with automated or semi-automatedmedication infusion pumps of the external or implantable type asdescribed, e.g., in U.S. Pat. No. 4,562,751; 4,678,408; 4,685,903 or4,573,994, to control delivery of insulin to a diabetic patient.

Particular embodiments of the flexible electrochemical sensor 12 areconstructed in accordance with thin film mask techniques to includeelongated thin film conductors embedded or encased between layers of aselected insulative material such as polyimide film or sheet, andmembranes. The sensor electrodes 20 at a tip end of the sensing portion18 are exposed through one of the insulative layers for direct contactwith patient blood or other body fluids, when the sensing portion 18 (oractive portion) of the sensor 12 is subcutaneously placed at aninsertion site. The sensing portion 18 is joined to a connection portion24 that terminates in conductive contact pads, or the like, which arealso exposed through one of the insulative layers. In alternativeembodiments, other types of implantable sensors, such as chemical based,optical based, or the like, may be used.

As is known in the art, the connection portion 24 and the contact padsare generally adapted for a direct wired electrical connection to asuitable monitor or sensor electronics device 100 for monitoring auser's condition in response to signals derived from the sensorelectrodes 20. Further description of flexible thin film sensors of thisgeneral type may be found, e.g., in U.S. Pat. No. 5,391,250, which isherein incorporated by reference. The connection portion 24 may beconveniently connected electrically to the monitor or sensor electronicsdevice 100 or by a connector block 28 (or the like) as shown anddescribed, e.g., in U.S. Pat. No. 5,482,473, which is also hereinincorporated by reference. Thus, in accordance with embodiments of thepresent invention, subcutaneous sensor sets 10 may be configured orformed to work with either a wired or a wireless characteristic monitorsystem.

The sensor electrodes 20 may be used in a variety of sensingapplications and may be configured in a variety of ways. For example,the sensor electrodes 20 may be used in physiological parameter sensingapplications in which some type of biomolecule is used as a catalyticagent. For example, the sensor electrodes 20 may be used in a glucoseand oxygen sensor having a glucose oxidase (GOx) enzyme catalyzing areaction with the sensor electrodes 20. The reaction produces GluconicAcid (C₆H₁₂O₇) and Hydrogen Peroxide (H₂O₂) in proportion to the amountof glucose present.

The sensor electrodes 20, along with a biomolecule or some othercatalytic agent, may be placed in a human body in a vascular ornon-vascular environment. For example, the sensor electrodes 20 andbiomolecule may be placed in a vein and be subjected to a blood stream,or may be placed in a subcutaneous or peritoneal region of the humanbody.

The monitor 100 may also be referred to as a sensor electronics device100. The monitor 100 may include a power source 110, a sensor interface122, processing electronics 124, and data formatting electronics 128.The monitor 100 may be coupled to the sensor set 10 by a cable 102through a connector that is electrically coupled to the connector block28 of the connection portion 24. In an alternative embodiment, the cablemay be omitted. In this embodiment of the invention, the monitor 100 mayinclude an appropriate connector for direct connection to the connectionportion 104 of the sensor set 10. The sensor set 10 may be modified tohave the connector portion 104 positioned at a different location, e.g.,on top of the sensor set to facilitate placement of the monitor 100 overthe sensor set.

In embodiments of the invention, the sensor interface 122, theprocessing electronics 124, and the data formatting electronics 128 areformed as separate semiconductor chips, however, alternative embodimentsmay combine the various semiconductor chips into a single or multiplecustomized semiconductor chips. The sensor interface 122 connects withthe cable 102 that is connected with the sensor set 10.

The power source 110 may be a battery. The battery can include threeseries silver oxide 357 battery cells. In alternative embodiments,different battery chemistries may be utilized, such as lithium basedchemistries, alkaline batteries, nickel metalhydride, or the like, and adifferent number of batteries may be used. The monitor 100 providespower to the sensor set via the power source 110, through the cable 102and cable connector 104. In an embodiment of the invention, the power isa voltage provided to the sensor set 10. In an embodiment of theinvention, the power is a current provided to the sensor set 10. In anembodiment of the invention, the power is a voltage provided at aspecific voltage to the sensor set 10.

FIGS. 2A and 2B illustrate an implantable sensor and electronics fordriving the implantable sensor according to an embodiment of the presentinvention. FIG. 2A shows a substrate 220 having two sides, a first side222 of which contains an electrode configuration and a second side 224of which contains electronic circuitry. As may be seen in FIG. 2A, afirst side 222 of the substrate comprises two counter electrode-workingelectrode pairs 240, 242, 244, 246 on opposite sides of a referenceelectrode 248. A second side 224 of the substrate comprises electroniccircuitry. As shown, the electronic circuitry may be enclosed in ahermetically sealed casing 226, providing a protective housing for theelectronic circuitry. This allows the sensor substrate 220 to beinserted into a vascular environment or other environment which maysubject the electronic circuitry to fluids. By sealing the electroniccircuitry in a hermetically sealed casing 226, the electronic circuitrymay operate without risk of short circuiting by the surrounding fluids.Also shown in FIG. 2A are pads 228 to which the input and output linesof the electronic circuitry may be connected. The electronic circuitryitself may be fabricated in a variety of ways. According to anembodiment of the present invention, the electronic circuitry may befabricated as an integrated circuit using techniques common in theindustry.

FIG. 2B illustrates a general block diagram of an electronic circuit forsensing an output of a sensor according to an embodiment of theinvention. At least one pair of sensor electrodes 310 may interface to adata converter 312, the output of which may interface to a counter 314.The counter 314 may be controlled by control logic 316. The output ofthe counter 314 may connect to a line interface 318. The line interface318 may be connected to input and output lines 320 and may also connectto the control logic 316. The input and output lines 320 may also beconnected to a power rectifier 322.

The sensor electrodes 310 may be used in a variety of sensingapplications and may be configured in a variety of ways. For example,the sensor electrodes 310 may be used in physiological parameter sensingapplications in which some type of biomolecule is used as a catalyticagent. For example, the sensor electrodes 310 may be used in a glucoseand oxygen sensor having a glucose oxidase (GOx) enzyme catalyzing areaction with the sensor electrodes 310. The sensor electrodes 310,along with a biomolecule or some other catalytic agent, may be placed ina human body in a vascular or non-vascular environment. For example, thesensor electrodes 310 and biomolecule may be placed in a vein and besubjected to a blood stream.

FIG. 3 illustrates a block diagram of a sensor electronics device and asensor including a plurality of electrodes according to an embodiment ofthe invention. The sensor set or system 350 includes a sensor 355 and asensor electronics device 360. The sensor 355 includes a counterelectrode 365, a reference electrode 370, and a working electrode 375.The sensor electronics device 360 includes a power supply 380, aregulator 385, a signal processor 390, a measurement processor 395, anda display/transmission module 397. The power supply 380 provides power(in the form of either a voltage, a current, or a voltage including acurrent) to the regulator 385. The regulator 385 transmits a regulatedvoltage to the sensor 355. In an embodiment of the invention, theregulator 385 transmits a voltage to the counter electrode 365 of thesensor 355.

The sensor 355 creates a sensor signal indicative of a concentration ofa physiological characteristic being measured. For example, the sensorsignal may be indicative of a blood glucose reading. In an embodiment ofthe invention utilizing subcutaneous sensors, the sensor signal mayrepresent a level of hydrogen peroxide in a subject. In an embodiment ofthe invention where blood or cranial sensors are utilized, the amount ofoxygen is being measured by the sensor and is represented by the sensorsignal. In an embodiment of the invention utilizing implantable orlong-term sensors, the sensor signal may represent a level of oxygen inthe subject. The sensor signal may be measured at the working electrode375. In an embodiment of the invention, the sensor signal may be acurrent measured at the working electrode. In an embodiment of theinvention, the sensor signal may be a voltage measured at the workingelectrode.

The signal processor 390 receives the sensor signal (e.g., a measuredcurrent or voltage) after the sensor signal is measured at the sensor355 (e.g., the working electrode). The signal processor 390 processesthe sensor signal and generates a processed sensor signal. Themeasurement processor 395 receives the processed sensor signal andcalibrates the processed sensor signal utilizing reference values. In anembodiment of the invention, the reference values are stored in areference memory and provided to the measurement processor 395. Themeasurement processor 395 generates sensor measurements. The sensormeasurements may be stored in a measurement memory (not shown). Thesensor measurements may be sent to a display/transmission device to beeither displayed on a display in a housing with the sensor electronicsor transmitted to an external device.

The sensor electronics device 360 may be a monitor which includes adisplay to display physiological characteristics readings. The sensorelectronics device 360 may also be installed in a desktop computer, apager, a television including communications capabilities, a laptopcomputer, a server, a network computer, a personal digital assistant(PDA), a portable telephone including computer functions, an infusionpump including a display, a glucose sensor including a display, and/or acombination infusion pump/glucose sensor. The sensor electronics device360 may be housed in a cellular phone, a smartphone, a network device, ahome network device, and/or other appliance connected to a home network.

FIG. 4 illustrates an alternative embodiment including a sensor and asensor electronics device. The sensor set or sensor system 400 includesa sensor electronics device 360 and a sensor 355. The sensor includes acounter electrode 365, a reference electrode 370, and a workingelectrode 375. The sensor electronics device 360 includes amicrocontroller 410 and a digital-to-analog converter (DAC) 420. Thesensor electronics device 360 may also include a current-to-frequencyconverter (I/F converter) 430.

The microcontroller 410 includes software program code, which whenexecuted, or programmable logic which, causes the microcontroller 410 totransmit a signal to the DAC 420, where the signal is representative ofa voltage level or value that is to be applied to the sensor 355. TheDAC 420 receives the signal and generates the voltage value at the levelinstructed by the microcontroller 410. In embodiments of the invention,the microcontroller 410 may change the representation of the voltagelevel in the signal frequently or infrequently. Illustratively, thesignal from the microcontroller 410 may instruct the DAC 420 to apply afirst voltage value for one second and a second voltage value for twoseconds.

The sensor 355 may receive the voltage level or value. In an embodimentof the invention, the counter electrode 365 may receive the output of anoperational amplifier which has as inputs the reference voltage and thevoltage value from the DAC 420. The application of the voltage levelcauses the sensor 355 to create a sensor signal indicative of aconcentration of a physiological characteristic being measured. In anembodiment of the invention, the microcontroller 410 may measure thesensor signal (e.g., a current value) from the working electrode.Illustratively, a sensor signal measurement circuit 431 may measure thesensor signal. In an embodiment of the invention, the sensor signalmeasurement circuit 431 may include a resistor and the current may bepassed through the resistor to measure the value of the sensor signal.In an embodiment of the invention, the sensor signal may be a currentlevel signal and the sensor signal measurement circuit 431 may be acurrent-to-frequency (I/F) converter 430. The current-to-frequencyconverter 430 may measure the sensor signal in terms of a currentreading, convert it to a frequency-based sensor signal, and transmit thefrequency-based sensor signal to the microcontroller 410. In embodimentsof the invention, the microcontroller 410 may be able to receivefrequency-based sensor signals easier than non-frequency-based sensorsignals. The microcontroller 410 receives the sensor signal, whetherfrequency-based or non frequency-based, and determines a value for thephysiological characteristic of a subject, such as a blood glucoselevel. The microcontroller 410 may include program code, which whenexecuted or run, is able to receive the sensor signal and convert thesensor signal to a physiological characteristic value. In oneembodiment, the microcontroller 410 may convert the sensor signal to ablood glucose level. In some embodiments, the microcontroller 410 mayutilize measurements stored within an internal memory in order todetermine the blood glucose level of the subject. In some embodiments,the microcontroller 410 may utilize measurements stored within a memoryexternal to the microcontroller 410 to assist in determining the bloodglucose level of the subject.

After the physiological characteristic value is determined by themicrocontroller 410, the microcontroller 410 may store measurements ofthe physiological characteristic values for a number of time periods.For example, a blood glucose value may be sent to the microcontroller410 from the sensor every second or five seconds, and themicrocontroller may save sensor measurements for five minutes or tenminutes of BG readings. The microcontroller 410 may transfer themeasurements of the physiological characteristic values to a display onthe sensor electronics device 360. For example, the sensor electronicsdevice 360 may be a monitor which includes a display that provides ablood glucose reading for a subject. In one embodiment, themicrocontroller 410 may transfer the measurements of the physiologicalcharacteristic values to an output interface of the microcontroller 410.The output interface of the microcontroller 410 may transfer themeasurements of the physiological characteristic values, e.g., bloodglucose values, to an external device, e.g., an infusion pump, acombined infusion pump/glucose meter, a computer, a personal digitalassistant, a pager, a network appliance, a server, a cellular phone, orany computing device.

FIG. 5 illustrates an electronic block diagram of the sensor electrodesand a voltage being applied to the sensor electrodes according to oneembodiment. In the embodiment illustrated in FIG. 5, an op amp 530 orother servo controlled device may connect to sensor electrodes 510through a circuit/electrode interface 538. The op amp 530, utilizingfeedback through the sensor electrodes, attempts to maintain aprescribed voltage (what the DAC may desire the applied voltage to be)between a reference electrode 532 and a working electrode 534 byadjusting the voltage at a counter electrode 536. Current may then flowfrom a counter electrode 536 to a working electrode 534. Such currentmay be measured to ascertain the electrochemical reaction between thesensor electrodes 510 and the biomolecule of a sensor that has beenplaced in the vicinity of the sensor electrodes 510 and used as acatalyzing agent. The circuitry disclosed in FIG. 5 may be utilized in along-term or implantable sensor or may be utilized in a short-term orsubcutaneous sensor.

In a long-term sensor embodiment, where a glucose oxidase (GOx) enzymeis used as a catalytic agent in a sensor, current may flow from thecounter electrode 536 to a working electrode 534 only if there is oxygenin the vicinity of the enzyme and the sensor electrodes 510.Illustratively, if the voltage set at the reference electrode 532 ismaintained at about 0.5 volts, the amount of current flowing from thecounter electrode 536 to a working electrode 534 has a fairly linearrelationship with unity slope to the amount of oxygen present in thearea surrounding the enzyme and the electrodes. Thus, increased accuracyin determining an amount of oxygen in the blood may be achieved bymaintaining the reference electrode 532 at about 0.5 volts and utilizingthis region of the current-voltage curve for varying levels of bloodoxygen. Different embodiments may utilize different sensors havingbiomolecules other than a glucose oxidase enzyme and may, therefore,have voltages other than 0.5 volts set at the reference electrode.

As discussed above, during initial implantation or insertion of thesensor 510, the sensor 510 may provide inaccurate readings due to theadjusting of the subject to the sensor and also electrochemicalbyproducts caused by the catalyst utilized in the sensor. Astabilization period is needed for many sensors in order for the sensor510 to provide accurate readings of the physiological parameter of thesubject. During the stabilization period, the sensor 510 does notprovide accurate blood glucose measurements. Users and manufacturers ofthe sensors may desire to improve the stabilization timeframe for thesensor so that the sensors can be utilized quickly after insertion intothe subject's body or a subcutaneous layer of the subject.

In previous sensor electrode systems, the stabilization period ortimeframe may have been within the one-hour to three-hours range. Inorder to decrease the stabilization period or timeframe and increase thetimeliness of accuracy of the sensor, a sensor (or electrodes of asensor) may be subjected to a number of pulses rather than theapplication of one pulse followed by the application of another voltage.FIG. 6A illustrates one method of applying pulses during a stabilizationtimeframe in order to reduce the stabilization timeframe. In thisembodiment, a voltage application device applies 600 a first voltage toan electrode for a first time or time period. In one embodiment, thefirst voltage may be a DC constant voltage. This results in an anodiccurrent being generated. In an alternative embodiment, adigital-to-analog converter or another voltage source may supply thevoltage to the electrode for a first time period. The anodic currentmeans that electrons are being driven towards the electrode to which thevoltage is applied. In certain embodiments, an application device mayapply a current instead of a voltage. In embodiments where a voltage isapplied to a sensor, after the application of the first voltage to theelectrode, the voltage regulator may wait (i.e., not apply a voltage)for a second time, timeframe, or time period 605. In other words, thevoltage application device waits until a second time period elapses. Thenon-application of voltage results in a cathodic current, which resultsin the gaining of electrons by the electrode to which the voltage is notapplied. The application of the first voltage to the electrode for afirst time period followed by the non-application of voltage for asecond time period is repeated 610 for a number of iterations. This maybe referred to as an anodic and cathodic cycle. In one embodiment, thenumber of total iterations of the stabilization method is three, i.e.,three applications of the voltage for the first time period, eachfollowed by no application of the voltage for the second time period. Inan embodiment, the first voltage may be 1.07 volts. In additionalembodiments, the first voltage may be 0.535 volts, or it may beapproximately 0.7 volts.

The repeated application of the voltage and the non-application of thevoltage results in the sensor (and thus the electrodes) being subjectedto an anodic-cathodic cycle. The anodic-cathodic cycle results in thereduction of electrochemical byproducts which are generated by apatient's body reacting to the insertion of the sensor or the implantingof the sensor. The electrochemical byproducts cause generation of abackground current, which results in inaccurate measurements of thephysiological parameter of the subject. Under certain operatingconditions, the electrochemical byproducts may be eliminated. Underother operating conditions, the electrochemical byproducts may bereduced or significantly reduced. A successful stabilization methodresults in the anodic-cathodic cycle reaching equilibrium,electrochemical byproducts being significantly reduced, and backgroundcurrent being minimized.

In one embodiment, the first voltage being applied to the electrode ofthe sensor may be a positive voltage. In an alternative embodiment, thefirst voltage being applied may be a negative voltage. Moreover, thefirst voltage may be applied to a working electrode. In someembodiments, the first voltage may be applied to the counter electrodeor the reference electrode.

In some embodiments, the duration of the voltage pulse and thenon-application of voltage may be equal, e.g., such as three minuteseach. In other embodiments, the duration of the voltage application orvoltage pulse may be different values, e.g., the first time and thesecond time may be different. In one embodiment, the first time periodmay be five minutes and the waiting period may be two minutes. In avariation, the first time period may be two minutes and the waitingperiod (or second timeframe) may be five minutes. In other words, theduration for the application of the first voltage may be two minutes andthere may be no voltage applied for five minutes. This timeframe is onlymeant to be illustrative and should not be limiting. For example, afirst timeframe may be two, three, five or ten minutes and the secondtimeframe may be five minutes, ten minutes, twenty minutes, or the like.The timeframes (e.g., the first time and the second time) may depend onunique characteristics of different electrodes, the sensors, and/or thepatient's physiological characteristics.

In connection with the foregoing, more or less than three pulses may beutilized to stabilize the glucose sensor. In other words, the number ofiterations may be greater than 3 or less than 3. For example, fourvoltage pulses (e.g., a high voltage followed by no voltage) may beapplied to one of the electrodes or six voltage pulses may be applied toone of the electrodes.

Illustratively, three consecutive pulses of 1.07 volts (followed byrespective waiting periods) may be sufficient for a sensor implantedsubcutaneously. In one embodiment, three consecutive voltage pulses of0.7 volts may be utilized. The three consecutive pulses may have ahigher or lower voltage value, either negative or positive, for a sensorimplanted in blood or cranial fluid, e.g., the long-term or permanentsensors. In addition, more than three pulses (e.g., five, eight, twelve)may be utilized to create the anodic-cathodic cycling between anodic andcathodic currents in any of the subcutaneous, blood, or cranial fluidsensors.

FIG. 6B illustrates a method of stabilizing sensors according to anembodiment of the inventions herein. In the embodiment illustrated inFIG. 6B, a voltage application device may apply 630 a first voltage tothe sensor for a first time to initiate an anodic cycle at an electrodeof the sensor. The voltage application device may be a DC power supply,a digital-to-analog converter, or a voltage regulator. After the firsttime period has elapsed, a second voltage is applied 635 to the sensorfor a second time to initiate a cathodic cycle at an electrode of thesensor. Illustratively, rather than no voltage being applied, as isillustrated in the method of FIG. 6A, a different voltage (from thefirst voltage) is applied to the sensor during the second timeframe. Inan embodiment of the invention, the application of the first voltage forthe first time and the application of the second voltage for the secondtime is repeated 640 for a number of iterations. In certain embodiments,the application of the first voltage for the first time and theapplication of the second voltage for the second time may each beapplied for a stabilization timeframe, e.g., 10 minutes, 15 minutes, or20 minutes rather than for a number of iterations. This stabilizationtimeframe is the entire timeframe for the stabilization sequence, e.g.,until the sensor (and electrodes) are stabilized. The benefit of thisstabilization methodology is a faster run-in of the sensors, lessbackground current (in other words a suppression of some the backgroundcurrent), and a better glucose response.

In one embodiment, the first voltage may be 0.535 volts applied for fiveminutes, the second voltage may be 1.070 volts applied for two minutes,the first voltage of 0.535 volts may be applied for five minutes, thesecond voltage of 1.070 volts may be applied for two minutes, the firstvoltage of 0.535 volts may be applied for five minutes, and the secondvoltage of 1.070 volts may be applied for two minutes. In other words,in this embodiment, there are three iterations of the voltage pulsingscheme. The pulsing methodology may be changed in that the secondtimeframe, e.g., the timeframe of the application of the second voltagemay be lengthened from two minutes to five minutes, ten minutes, fifteenminutes, or twenty minutes. In addition, after the three iterations areapplied in this embodiment of the invention, a nominal working voltageof 0.535 volts may be applied.

The 1.070 and 0.535 volts are illustrative values. Other voltage valuesmay be selected based on a variety of factors. These factors may includethe type of enzyme utilized in the sensor, the membranes utilized in thesensor, the operating period of the sensor, the length of the pulse,and/or the magnitude of the pulse. Under certain operating conditions,the first voltage may be in a range of 1.00 to 1.09 volts and the secondvoltage may be in a range of 0.510 to 0.565 volts. In other operatingembodiments, the ranges that bracket the first voltage and the secondvoltage may have a higher range, e.g., 0.3 volts, 0.6 volts, 0.9 volts,depending on the voltage sensitivity of the electrode in the sensor.Under other operating conditions, the voltage may be in a range of 0.8volts to 1.34 volts and the other voltage may be in a range of 0.335 to0.735. Under other operating conditions, the range of the higher voltagemay be smaller than the range of the lower voltage. Illustratively, thehigher voltage may be in a range of 0.9 to 1.09 volts and the lowervoltage may be in a range of 0.235 to 0.835 volts.

In an embodiment, the first voltage and the second voltage may bepositive voltages, or alternatively in other embodiments, negativevoltages. In another embodiment, the first voltage may be positive andthe second voltage may be negative, or alternatively, the first voltagemay be negative and the second voltage may be positive. The firstvoltage may be different voltage levels for each of the iterations. Inaddition, the first voltage may be a D.C. constant voltage. Moreover,the first voltage may be a ramp voltage, a sinusoid-shaped voltage, astepped voltage, or other commonly utilized voltage waveforms. In anembodiment, the second voltage may be a D.C. constant voltage, a rampvoltage, a sinusoid-shaped voltage, a stepped voltage, or other commonlyutilized voltage waveforms. In alternative embodiments, the firstvoltage or the second voltage may be an AC signal riding on a DCwaveform. In general, the first voltage may be one type of voltage,e.g., a ramp voltage, and the second voltage may be a second type ofvoltage, e.g., a sinusoid-shaped voltage, and the first voltage (or thesecond voltage) may have different waveform shapes for each of theiterations. For example, if there are three cycles in a stabilizationmethod, in a first cycle, the first voltage may be a ramp voltage, inthe second cycle, the first voltage may be a constant voltage, and inthe third cycle, the first voltage may be a sinusoidal voltage.

In an embodiment, the duration of the first timeframe and the durationof the second timeframe may have the same value, or alternatively, theduration of the first timeframe and the second timeframe may havedifferent values. For example, the duration of the first timeframe maybe two minutes and the duration of the second timeframe may be fiveminutes and the number of iterations may be three. As discussed above,the stabilization method may include a number of iterations. In variousembodiments, during different iterations of the stabilization method,the duration of each of the first timeframes may change and the durationof each of the second timeframes may change. Illustratively, during thefirst iteration of the anodic-cathodic cycling, the first timeframe maybe 2 minutes and the second timeframe may be 5 minutes. During thesecond iteration, the first timeframe may be 1 minute and the secondtimeframe may be 3 minutes. During the third iteration, the firsttimeframe may be 3 minutes and the second timeframe may be 10 minutes.

In one embodiment, a first voltage of 0.535 volts is applied to anelectrode in a sensor for two minutes to initiate an anodic cycle, thena second voltage of 1.07 volts is applied to the electrode for fiveminutes to initiate a cathodic cycle. The first voltage of 0.535 voltsis then applied again for two minutes to initiate the anodic cycle and asecond voltage of 1.07 volts is applied to the sensor for five minutes.In a third iteration, 0.535 volts is applied for two minutes to initiatethe anodic cycle and then 1.07 volts is applied for five minutes. Thevoltage applied to the sensor is then 0.535 during the actual workingtimeframe of the sensor, e.g., when the sensor provides readings of aphysiological characteristic of a subject.

Shorter duration voltage pulses may be utilized in the embodiment ofFIGS. 6A and 6B. The shorter duration voltage pulses may be utilized toapply the first voltage, the second voltage, or both. In one embodiment,the magnitude of the shorter duration voltage pulse for the firstvoltage is −1.07 volts and the magnitude of the shorter duration voltagepulse for the second voltage is approximately half of the highmagnitude, e.g., −0.535 volts. Alternatively, the magnitude of theshorter duration pulse for the first voltage may be 0.535 volts and themagnitude of the shorter duration pulse for the second voltage is 1.07volts.

In embodiments utilizing short duration pulses, the voltage may not beapplied continuously for the entire first time period. Instead, thevoltage application device may transmit a number of short durationpulses during the first time period. In other words, a number ofmini-width or short duration voltage pulses may be applied to theelectrodes of the sensor over the first time period. Each mini-width orshort duration pulse may have a width of a number of milliseconds.Illustratively, this pulse width may be 30 milliseconds, 50milliseconds, 70 milliseconds or 200 milliseconds. These values aremeant to be illustrative and not limiting. In one embodiment, such asthe embodiment illustrated in FIG. 6A, these short duration pulses areapplied to the sensor (electrode) for the first time period and then novoltage is applied for the second time period.

Each short duration pulse may have the same time duration within thefirst time period. For example, each short duration voltage pulse mayhave a time width of 50 milliseconds and each pulse delay between thepulses may be 950 milliseconds. In this example, if two minutes is themeasured time for the first timeframe, then 120 short duration voltagepulses may be applied to the sensor. Alternatively, each of the shortduration voltage pulses may have different time durations. In variousembodiments, each of the short duration voltage pulses may have the sameamplitude values, or may have different amplitude values. By utilizingshort duration voltage pulses rather than a continuous application ofvoltage to the sensor, the same anodic and cathodic cycling may occurand the sensor (e.g., electrodes) is subjected to less total energy orcharge over time. The use of short duration voltage pulses utilizes lesspower as compared to the application of continuous voltage to theelectrodes because there is less energy applied to the sensors (and thusthe electrodes).

FIG. 6C illustrates utilization of feedback in stabilizing the sensoraccording to one embodiment. The sensor system may include a feedbackmechanism to determine if additional pulses are needed to stabilize asensor. In one embodiment, a sensor signal generated by an electrode(e.g., a working electrode) may be analyzed to determine if the sensorsignal is stabilized. A first voltage is applied 630 to an electrode fora first timeframe to initiate an anodic cycle. A second voltage isapplied 635 to an electrode for a second timeframe to initiate acathodic cycle. In embodiments of the inventions herein, an analyzationmodule may analyze a sensor signal (e.g., the current emitted by thesensor signal, a resistance at a specific point in the sensor, animpedance at a specific node in the sensor) and determine if a thresholdmeasurement has been reached 637 (e.g., determining if the sensor isproviding accurate readings by comparing against the thresholdmeasurement). If the sensor readings are determined to be accurate,which represents that the electrode (and thus the sensor) is stabilized642, no additional application of the first voltage and/or the secondvoltage may be generated. If stability was not achieved, then anadditional anodic/cathodic cycle may be initiated by the application 630of a first voltage to an electrode for a first time period and then theapplication 635 of the second voltage to the electrode for a second timeperiod.

In some embodiments, the analyzation module may be employed after ananodic/cathodic cycle of three applications of the first voltage and thesecond voltage to an electrode of the sensor. However, an analyzationmodule may be employed after one application of the first voltage andthe second voltage, as is illustrated in FIG. 6C.

The analyzation module may be utilized to measure a voltage emittedafter a current has been introduced across an electrode or across twoelectrodes. The analyzation module may monitor a voltage level at theelectrode or at the receiving level. In one embodiment, if the voltagelevel is above a certain threshold, this may mean that the sensor isstabilized. In one embodiment, if the voltage level falls below athreshold level, this may indicate that the sensor is stabilized andready to provide readings. In one embodiment, a current may beintroduced to an electrode or across a couple of electrodes. Theanalyzation module may monitor a current level emitted from theelectrode. In this embodiment, the analyzation module may be able tomonitor the current if the current is different by an order of magnitudefrom the sensor signal current. If the current is above or below acurrent threshold, this may signify that the sensor is stabilized.

In an embodiment of the inventions herein, the analyzation module maymeasure an impedance between two electrodes of the sensor. Theanalyzation module may compare the impedance against a threshold ortarget impedance value and if the measured impedance is lower than thetarget or threshold impedance, the sensor (and hence the sensor signal)may be stabilized. In one embodiment, the analyzation module may measurea resistance between two electrodes of the sensor. In this embodiment ofthe invention, if the analyzation module compares the resistance againsta threshold or target resistance value and the measured resistance valueis less than the threshold or target resistance value, then theanalyzation module may determine that the sensor is stabilized and thatthe sensor signal may be utilized.

FIG. 7 illustrates an effect of stabilizing a sensor according to anembodiment of the invention. Line 705 represents blood glucose sensorreadings for a glucose sensor where a previous single pulsestabilization method was utilized. Line 710 represents blood glucosereadings for a glucose sensor where three voltage pulses are applied(e.g., 3 voltage pulses having a duration of 2 minutes each followed by5 minutes of no voltage being applied). The x-axis 715 represents anamount of time. The dots 720, 725, 730, and 735 represent measuredglucose readings, taken utilizing a finger stick and then input into aglucose meter. As illustrated by the graph, the previous single pulsestabilization method took approximately 1 hour and 30 minutes in orderto stabilize to the desired glucose reading, e.g., 100 units. Incontrast, the three pulse stabilization method took only approximately15 minutes to stabilize the glucose sensor and results in a drasticallyimproved stabilization timeframe.

FIG. 8A illustrates a block diagram of a sensor electronics device and asensor including a voltage generation device. The voltage generation orapplication device 810 includes electronics, logic, or circuits whichgenerate voltage pulses. The sensor electronics device 360 may alsoinclude an input device 820 to receive reference values and other usefuldata. In one embodiment, the sensor electronics device may include ameasurement memory 830 to store sensor measurements. In this embodiment,the power supply 380 may supply power to the sensor electronics device.The power supply 380 may supply power to a regulator 385, which suppliesa regulated voltage to the voltage generation or application device 810.The connection terminals 811 represent that in the illustratedembodiment, the connection terminal couples or connects the sensor 355to the sensor electronics device 360.

In the embodiment illustrated in FIG. 8A, the voltage generation orapplication device 810 supplies a voltage, e.g., the first voltage orthe second voltage, to an input terminal of an operational amplifier840. The voltage generation or application device 810 may also supplythe voltage to a working electrode 375 of the sensor 355. Another inputterminal of the operational amplifier 840 is coupled to the referenceelectrode 370 of the sensor. The application of the voltage from thevoltage generation or application device 810 to the operationalamplifier 840 drives a voltage measured at the counter electrode 365 tobe close to or equal to the voltage applied at the working electrode375. In an embodiment, the voltage generation or application device 810could be utilized to apply the desired voltage between the counterelectrode and the working electrode. This may occur by the applicationof the fixed voltage to the counter electrode directly.

In one embodiment as illustrated in FIGS. 6A and 6B, the voltagegeneration device 810 generates a first voltage that is to be applied tothe sensor during a first timeframe. The voltage generation device 810transmits this first voltage to an op amp 840 which drives the voltageat a counter electrode 365 of the sensor 355 to the first voltage. Insome embodiments, the voltage generation device 810 also could transmitthe first voltage directly to the counter electrode 365 of the sensor355. In the embodiment illustrated in FIG. 6A, the voltage generationdevice 810 then does not transmit the first voltage to the sensor 355for a second timeframe. In other words, the voltage generation device810 is turned off or switched off. The voltage generation device 810 maybe programmed to continue cycling between applying the first voltage andnot applying a voltage for either a number of iterations or for astabilization timeframe, e.g., for twenty minutes. FIG. 8B illustrates avoltage generation device to implement this embodiment of the invention.The voltage regulator 385 transfers the regulated voltage to the voltagegeneration device 810. A control circuit 860 controls the closing andopening of a switch 850. If the switch 850 is closed, the voltage isapplied. If the switch 850 is opened, the voltage is not applied. Thetimer 865 provides a signal to the control circuit 860 to instruct thecontrol circuit 860 to turn on and off the switch 850. The controlcircuit 860 includes logic which can instruct the circuit to open andclose the switch 850 a number of times (to match the necessaryiterations). In one embodiment, the timer 865 may also transmit astabilization signal to identify that the stabilization sequence iscompleted, i.e., that a stabilization timeframe has elapsed.

In one embodiment, the voltage generation device generates a firstvoltage for a first timeframe and generates a second voltage for asecond timeframe. FIG. 8C illustrates a voltage generation device togenerate two voltage values to implement this embodiment. In thisembodiment, a two position switch 870 is utilized. Illustratively, ifthe first switch position 871 is turned on or closed by the timer 865instructing the control circuit 860, then the voltage generation device810 generates a first voltage for the first timeframe. After the firstvoltage has been applied for the first timeframe, the timer sends asignal to the control circuit 860 indicating the first timeframe haselapsed and the control circuit 860 directs the switch 870 to move tothe second position 872. When the switch 870 is at the second position872, the regulated voltage is directed to a voltage step-down or buckconverter 880 to reduce the regulated voltage to a lesser value. Thelesser value is then delivered to the op amp 840 for the secondtimeframe. After the timer 865 has sent a signal to the control circuit860 that the second timeframe has elapsed, the control circuit 860 movesthe switch 870 back to the first position. This continues until thedesired number of iterations has been completed or the stabilizationtimeframe has elapsed. In an embodiment of the inventions herein, afterthe sensor stabilization timeframe has elapsed, the sensor transmits asensor signal 350 to the signal processor 390.

FIG. 8D illustrates a voltage application device 810 utilized to performmore complex applications of voltage to the sensor. The voltageapplication device 810 may include a control device 860, a switch 890, asinusoid voltage generation device 891, a ramp voltage generation device892, and a constant voltage generation device 893. In other embodiments,the voltage application may generate an AC wave on top of a DC signal orother various voltage pulse waveforms. In the embodiment illustrated inFIG. 8D, the control device 860 may cause the switch to move to one ofthe three voltage generation systems 891 (sinusoid), 892 (ramp), 893(constant DC). This results in each of the voltage generation systemsgenerating the identified voltage waveform. Under certain operatingconditions, e.g., where a sinusoidal pulse is to be applied for threepulses, the control device 860 may cause the switch 890 to connect thevoltage from the voltage regulator 385 to the sinusoid voltage generator891 in order for the voltage application device 810 to generate asinusoidal voltage. Under other operating conditions, e.g., when a rampvoltage is applied to the sensor as the first voltage for a first pulseof three pulses, a sinusoid voltage is applied to the sensor as thefirst voltage for a second pulse of the three pulses, and a constant DCvoltage is applied to the sensor as the first voltage for a third pulseof the three pulses, the control device 860 may cause the switch 890,during the first timeframes in the anodic/cathodic cycles, to movebetween connecting the voltage from the voltage generation orapplication device 810 to the ramp voltage generation system 892, thento the sinusoidal voltage generation system 891, and then to theconstant DC voltage generation system 893. In this embodiment, thecontrol device 860 may also be directing or controlling the switch toconnect certain ones of the voltage generation subsystems to the voltagefrom the regulator 385 during the second timeframe, e.g., duringapplication of the second voltage.

FIG. 9A illustrates a sensor electronics device including amicrocontroller for generating voltage pulses. The advanced sensorelectronics device may include a microcontroller 410 (see FIG. 4), adigital-to-analog converter (DAC) 420, an op amp 840, and a sensorsignal measurement circuit 431. In one embodiment, the sensor signalmeasurement circuit may be a current-to-frequency (I/F) converter 430.In the embodiment illustrated in FIG. 9A, software or programmable logicin the microcontroller 410 provides instructions to transmit signals tothe DAC 420, which in turn instructs the DAC 420 to output a specificvoltage to the operational amplifier 840. The microcontroller 410 mayalso be instructed to output a specific voltage to the working electrode375, as is illustrated by line 911 in FIG. 9A. As discussed above, theapplication of the specific voltage to operational amplifier 840 and theworking electrode 375 may drive the voltage measured at the counterelectrode to the specific voltage magnitude. In other words, themicrocontroller 410 outputs a signal which is indicative of a voltage ora voltage waveform that is to be applied to the sensor 355 (e.g., theoperational amplifier 840 coupled to the sensor 355). In an alternativeembodiment, a fixed voltage may be set by applying a voltage directlyfrom the DAC 420 between the reference electrode and the workingelectrode 375. A similar result may also be obtained by applyingvoltages to each of the electrodes with the difference equal to thefixed voltage applied between the reference and working electrodes. Inaddition, the fixed voltage may be set by applying a voltage between thereference and the counter electrode. Under certain operating conditions,the microcontroller 410 may generate a pulse of a specific magnitudewhich the DAC 420 understands represents that a voltage of a specificmagnitude is to be applied to the sensor. After a first timeframe, themicrocontroller 410 (via the program or programmable logic) outputs asecond signal which either instructs the DAC 420 to output no voltage(for a sensor electronics device 360 operating according to the methoddescribed in FIG. 6A) or to output a second voltage (for a sensorelectronics device 360 operating according to the method described inFIG. 6B). The microcontroller 410, after the second timeframe haselapsed, then repeats the cycle of sending the signal indicative of afirst voltage to be applied (for the first timeframe) and then sendingthe signal to instruct no voltage is to be applied or that a secondvoltage is to be applied (for the second timeframe).

Under other operating conditions, the microcontroller 410 may generate asignal to the DAC 420 which instructs the DAC to output a ramp voltage.Under other operating conditions, the microcontroller 410 may generate asignal to the DAC 420 which instructs the DAC 420 to output a voltagesimulating a sinusoidal voltage. These signals could be incorporatedinto any of the pulsing methodologies discussed above in the precedingparagraph or earlier in the application. In one embodiment, themicrocontroller 410 may generate a sequence of instructions and/orpulses, which the DAC 420 receives and understands to mean that acertain sequence of pulses is to be applied. For example, themicrocontroller 410 may transmit a sequence of instructions (via signalsand/or pulses) that instruct the DAC 420 to generate a constant voltagefor a first iteration of a first timeframe, a ramp voltage for a firstiteration of a second timeframe, a sinusoidal voltage for a seconditeration of a first timeframe, and a squarewave having two values for asecond iteration of the second timeframe.

The microcontroller 410 may include programmable logic or a program tocontinue this cycling for a stabilization timeframe or for a number ofiterations. Illustratively, the microcontroller 410 may include countinglogic to identify when the first timeframe or the second timeframe haselapsed. Additionally, the microcontroller 410 may include countinglogic to identify that a stabilization timeframe has elapsed. After anyof the preceding timeframes have elapsed, the counting logic mayinstruct the microcontroller to either send a new signal or to stoptransmission of a signal to the DAC 420.

The use of the microcontroller 410 allows a variety of voltagemagnitudes to be applied in a number of sequences for a number of timedurations. In an embodiment of the invention, the microcontroller 410may include control logic or a program to instruct the digital-to-analogconverter 420 to transmit a voltage pulse having a magnitude ofapproximately 1.0 volt for a first time period of 1 minute, to thentransmit a voltage pulse having a magnitude of approximately 0.5 voltsfor a second time period of 4 minutes, and to repeat this cycle for fouriterations. In one embodiment, the microcontroller 420 may be programmedto transmit a signal to cause the DAC 420 to apply the same magnitudevoltage pulse for each first voltage in each of the iterations. Themicrocontroller 410 may be programmed to transmit a signal to cause theDAC to apply a different magnitude voltage pulse for each first voltagein each of the iterations. In this embodiment, the microcontroller 410may also be programmed to transmit a signal to cause the DAC 420 toapply a different magnitude voltage pulse for each second voltage ineach of the iterations. Illustratively, the microcontroller 410 may beprogrammed to transmit a signal to cause the DAC 420 to apply a firstvoltage pulse of approximately 1.0 volt in the first iteration, to applya second voltage pulse of approximately 0.5 volts in the firstiteration, to apply a first voltage of 0.7 volts and a second voltage of0.4 volts in the second iteration, and to apply a first voltage of 1.2volts and a second voltage of 0.8 volts in the third iteration.

The microcontroller 410 may also be programmed to instruct the DAC 420to provide a number of short duration voltage pulses for a firsttimeframe. In this embodiment of the invention, rather than one voltagebeing applied for the entire first timeframe (e.g., two minutes), anumber of shorter duration pulses may be applied to the sensor. In thisembodiment, the microcontroller 410 may also be programmed to instructthe DAC 420 to provide a number of short duration voltage pulses for thesecond timeframe to the sensor. Illustratively, the microcontroller 410may send a signal to cause the DAC to apply a number of short durationvoltage pulses where the short duration is 50 milliseconds or 100milliseconds. In between these short duration pulses the DAC may applyno voltage or the DAC may apply a minimal voltage. The microcontrollermay cause the DAC 420 to apply the short duration voltage pulses for thefirst timeframe, e.g., two minutes. The microcontroller 410 may thensend a signal to cause the DAC to either not apply any voltage or toapply the short duration voltage pulses at a magnitude of a secondvoltage for a second timeframe to the sensor, e.g., the second voltagemay be 0.75 volts and the second timeframe may be 5 minutes. In oneembodiment, the microcontroller 410 may send a signal to the DAC 420 tocause the DAC 420 to apply a different magnitude voltage for each of theshort duration pulses in the first timeframe and/or in the secondtimeframe. In an embodiment, the microcontroller 410 may send a signalto the DAC 420 to cause the DAC 420 to apply a pattern of voltagemagnitudes to the short durations voltage pulses for the first timeframeor the second timeframe. For example, the microcontroller may transmit asignal or pulses instructing the DAC 420 to apply thirty 20-millisecondpulses to the sensor during the first timeframe. Each of the thirty20-millisecond pulses may have the same magnitude or may have adifferent magnitude. In this embodiment, the microcontroller 410 mayinstruct the DAC 420 to apply short duration pulses during the secondtimeframe or may instruct the DAC 420 to apply another voltage waveformduring the second timeframe.

Although the disclosures in FIGS. 6-8 disclose the application of avoltage, a current may also be applied to the sensor to initiate thestabilization process. Illustratively, in the embodiment illustrated inFIG. 6B, a first current may be applied during a first timeframe toinitiate an anodic or cathodic response and a second current may beapplied during a second timeframe to initiate the opposite anodic orcathodic response. The application of the first current and the secondcurrent may continue for a number of iterations or may continue for astabilization timeframe. In one embodiment, a first current may beapplied during a first timeframe and a first voltage may be appliedduring a second timeframe. In other words, one of the anodic or cathodiccycles may be triggered by a current being applied to the sensor and theother of the anodic or cathodic cycles may be triggered by a voltagebeing applied to the sensor. As described above, a current applied maybe a constant current, a ramp current, a stepped pulse current, or asinusoidal current. Under certain operating conditions, the current maybe applied as a sequence of short duration pulses during the firsttimeframe.

FIG. 9B illustrates a sensor and sensor electronics utilizing ananalyzation module for feedback in a stabilization period according toan embodiment of the inventions herein. FIG. 9B introduces ananalyzation module 950 to the sensor electronics device 360. Theanalyzation module 950 utilizes feedback from the sensor to determinewhether or not the sensor is stabilized. In one embodiment, themicrocontroller 410 may include instructions or commands to control theDAC 420 so that the DAC 420 applies a voltage or current to a part ofthe sensor 355. FIG. 9B illustrates that a voltage or current could beapplied between a reference electrode 370 and a working electrode 375.However, the voltage or current can be applied in between electrodes ordirectly to one of the electrodes and the invention should not belimited by the embodiment illustrated in FIG. 9B. The application of thevoltage or current is illustrated by dotted line 955. The analyzationmodule 950 may measure a voltage, a current, a resistance, or animpedance in the sensor 355. FIG. 9B illustrates that the measurementoccurs at the working electrode 375, but this should not limit theinvention because other embodiments may measure a voltage, a current, aresistance, or an impedance in between electrodes of the sensor ordirectly at either the reference electrode 370 or the counter electrode365. The analyzation module 950 may receive the measured voltage,current, resistance, or impedance and may compare the measurement to astored value (e.g., a threshold value). Dotted line 956 represents theanalyzation module 950 reading or taking a measurement of the voltage,current, resistance, or impedance. Under certain operating conditions,if the measured voltage, current, resistance, or impedance is above thethreshold, the sensor is stabilized and the sensor signal is providingaccurate readings of a physiological condition of a patient. Under otheroperating conditions, if the measured voltage, current, resistance, orimpedance is below the threshold, the sensor is stabilized. Under otheroperating conditions, the analyzation module 950 may verify that themeasured voltage, current, resistance, or impedance is stable for aspecific timeframe, e.g., one minute or two minutes. This may representthat the sensor 355 is stabilized and that the sensor signal istransmitting accurate measurements of a subject's physiologicalparameter, e.g., blood glucose level. After the analyzation module 950has determined that the sensor is stabilized and the sensor signal isproviding accurate measurements, the analyzation module 950 may transmita signal (e.g., a sensor stabilization signal) to the microcontroller410 indicating that the sensor is stabilized and that themicrocontroller 410 can start using or receiving the sensor signal fromthe sensor 355. This is represented by dotted line 957.

FIG. 10 illustrates a block diagram of a sensor system includinghydration electronics. The sensor system includes a connector 1010, asensor 1012, and a monitor or sensor electronics device 1025. The sensor1012 includes electrodes 1020 and a connection portion 1024. In oneembodiment, the sensor 1012 may be connected to the sensor electronicsdevice 1025 via a connector 1010 and a cable. In other embodiments, thesensor 1012 may be directly connected to the sensor electronics device1025. In some embodiments, the sensor 1012 may be incorporated into thesame physical device as the sensor electronics device 1025. The monitoror sensor electronics device 1025 may include a power supply 1030, aregulator 1035, a signal processor 1040, a measurement processor 1045,and a processor 1050. The monitor or sensor electronics device 1025 mayalso include a hydration detection circuit 1060. The hydration detectioncircuit 1060 interfaces with the sensor 1012 to determine if theelectrodes 1020 of the sensor 1012 are sufficiently hydrated. If theelectrodes 1020 are not sufficiently hydrated, the electrodes 1020 donot provide accurate glucose readings, so it is important to know whenthe electrodes 1020 are sufficiently hydrated. Once the electrodes 1020are sufficiently hydrated, accurate glucose readings may be obtained.

In the embodiment illustrated in FIG. 10, the hydration detectioncircuit 1060 may include a delay or timer module 1065 and a connectiondetection module 1070. In an embodiment utilizing the short term sensoror the subcutaneous sensor, after the sensor 1012 has been inserted intothe subcutaneous tissue, the sensor electronics device or monitor 1025is connected to the sensor 1012. The connection detection module 1070identifies that the sensors electronics device 1025 has been connectedto the sensor 1012 and sends a signal to the timer module 1065. This isillustrated in FIG. 10 by the arrow 1084 which represents a detector1083 detecting a connection and sending a signal to the connectiondetection module 1070 indicating the sensor 1012 has been connected tothe sensor electronics device 1025. In an embodiment where implantableor long-term sensors are utilized, a connection detection module 1070identifies that the implantable sensor has been inserted into the body.The timer module 1065 receives the connection signal and waits a set orestablished hydration time. Illustratively, the hydration time may betwo minutes, five minutes, ten minutes, or 20 minutes. These examplesare meant to be illustrative and not to be limiting. The timeframe doesnot have to be a set number of minutes and can include any number ofseconds. In one embodiment, after the timer module 1065 has waited forthe set hydration time, the timer module 1065 may notify the processor1050 that the sensor 1012 is hydrated by sending a hydration signal,which is illustrated by line 1086.

In this embodiment, the processor 1050 may receive the hydration signaland only start utilizing the sensor signal (e.g., sensor measurements)after the hydration signal has been received. In another embodiment, thehydration detection circuit 1060 may be coupled between the sensor (thesensor electrodes 1020) and the signal processor 1040. In thisembodiment, the hydration detection circuit 1060 may prevent the sensorsignal from being sent to signal processor 1040 until the timer module1065 has notified the hydration detection circuit 1060 that the sethydration time has elapsed. This is illustrated by the dotted lineslabeled with reference numerals 1080 and 1081. Illustratively, the timermodule 1065 may transmit a connection signal to a switch (or transistor)to turn on the switch and let the sensor signal proceed to the signalprocessor 1040. In an alternative embodiment, the timer module 1065 maytransmit a connection signal to turn on a switch 1088 (or close theswitch 1088) in the hydration detection circuit 1060 to allow a voltagefrom the regulator 1035 to be applied to the sensor 1012 after thehydration time has elapsed. In other words, in this embodiment, thevoltage from the regulator 1035 is not applied to the sensor 1012 untilafter the hydration time has elapsed.

FIG. 11 illustrates an embodiment including a mechanical switch toassist in determining a hydration time. In one embodiment, a singlehousing may include a sensor assembly 1120 and a sensor electronicsdevice 1125. In another embodiment, the sensor assembly 1120 may be inone housing and the sensor electronics device 1125 may be in a separatehousing, but the sensor assembly 1120 and the sensor electronics device1125 may be connected together. In this embodiment, a connectiondetection mechanism 1160 may be a mechanical switch. The mechanicalswitch may detect that the sensor 1120 is physically connected to thesensor electronics device 1125. A timer circuit 1135 may also beactivated when the mechanical switch 1160 detects that the sensor 1120is connected to the sensor electronics device 1125. In other words, themechanical switch may close and a signal may be transferred to a timercircuit 1135. Once a hydration time has elapsed, the timer circuit 1135transmits a signal to the switch 1140 to allow the regulator 1035 toapply a voltage to the sensor 1120. In other words, no voltage isapplied until the hydration time has elapsed. In one embodiment, currentmay replace voltage as what is being applied to the sensor once thehydration time elapses. In an alternative embodiment, when themechanical switch 1160 identifies that a sensor 1120 has been physicallyconnected to the sensor electronics device 1125, power may initially beapplied to the sensor 1120. Power being sent to the sensor 1120 resultsin a sensor signal being output from the working electrode in the sensor1120. The sensor signal may be measured and sent to a processor 1175.The processor 1175 may include a counter input. Under certain operatingconditions, after a set hydration time has elapsed from when the sensorsignal was input into the processor 1175, the processor 1175 may startprocessing the sensor signal as an accurate measurement of the glucosein a subject's body. In other words, the processor 1170 has received thesensor signal from the potentiostat circuit 1170 for a certain amount oftime, but will not process the signal until receiving an instructionfrom the counter input of the processor identifying that a hydrationtime has elapsed. In an embodiment, the potentiostat circuit 1170 mayinclude a current-to-frequency converter 1180. In this embodiment, thecurrent-to-frequency converter 1180 may receive the sensor signal as acurrent value and may convert the current value into a frequency value,which is easier for the processor 1175 to handle.

The mechanical switch 1160 may also notify the processor 1175 when thesensor 1120 has been disconnected from the sensor electronics device1125. This is represented by dotted line 1176 in FIG. 11. This mayresult in the processor 1170 powering down or reducing power to a numberof components, chips, and/or circuits of the sensor electronics device1125. If the sensor 1120 is not connected, the battery or power sourcemay be drained if the components or circuits of the sensor electronicsdevice 1125 are in a power on state. Accordingly, if the mechanicalswitch 1160 detects that the sensor 1120 has been disconnected from thesensor electronics device 1125, the mechanical switch may indicate thisto the processor 1175, and the processor 1175 may power down or reducepower to one or more of the electronic circuits, chips, or components ofthe sensor electronics device 1125.

FIG. 12 illustrates an electrical method of detection of hydrationaccording to an embodiment of the inventions herein. In one embodiment,an electrical detecting mechanism for detecting connection of a sensormay be utilized. In this embodiment, the hydration detection electronics1250 may include an AC source 1255 and a detection circuit 1260. Thehydration detection electronics 1250 may be located in the sensorelectronics device 1225. The sensor 1220 may include a counter electrode1221, a reference electrode 1222, and a working electrode 1223. Asillustrated in FIG. 12, the AC source 1255 is coupled to a voltagesetting device 1275, the reference electrode 1222, and the detectioncircuit 1260. In this embodiment, an AC signal from the AC source isapplied to the reference electrode connection, as illustrated by dottedline 1291 in FIG. 12. The AC signal may be coupled to the sensor 1220through an impedance and the coupled signal is attenuated significantlyif the sensor 1220 is connected to the sensor electronics device 1225.Thus, a low level AC signal is present at an input to the detectioncircuit 1260. This may also be referred to as a highly attenuated signalor a signal with a high level of attenuation. Under certain operatingconditions, the voltage level of the AC signal may beVapplied*(Ccoupling)/(Ccoupling+Csensor). If the detection circuit 1260detects that a high level AC signal (lowly attenuated signal) is presentat an input terminal of the detection circuit 1260, no interrupt is sentto the microcontroller 410 because the sensor 1220 has not beensufficiently hydrated or activated. For example, the input of thedetection circuit 1260 may be a comparator. If the sensor 1220 issufficiently hydrated (or wetted), an effective capacitance formsbetween the counter electrode and the reference electrode (e.g.,capacitance C_(r-c) in FIG. 12), and an effective capacitance formsbetween the reference electrode and the working electrode (e.g.,capacitance C_(w-r) in FIG. 12). In other words, an effectivecapacitance relates to capacitance being formed between two nodes anddoes not represent that an actual capacitor is placed in a circuitbetween the two electrodes. In one embodiment, the AC signal from the ACsource 1255 is sufficiently attenuated by capacitances C_(r-c) andC_(w-r) and the detection circuit 1260 detects the presence of a lowlevel or highly attenuated AC signal from the AC source 1255 at theinput terminal of the detection circuit 1260. This embodiment issignificant because the utilization of the existing connections betweenthe sensor 1120 and the sensor electronics device 1125 reduces thenumber of connections to the sensor. In other words, the mechanicalswitch, disclosed in FIG. 11, requires a switch and associatedconnections between the sensor 1120 and the sensor electronics device1125. It is advantageous to eliminate the mechanical switch because thesensor 1120 is continuously shrinking in size and the elimination ofcomponents helps achieve this size reduction. In alternativeembodiments, the AC signal may be applied to different electrodes (e.g.,the counter electrode or the working electrode) and the invention mayoperate in a similar fashion.

As noted above, after the detection circuit 1260 has detected that a lowlevel AC signal is present at the input terminal of the detectioncircuit 1260, the detection circuit 1260 may later detect that a highlevel AC signal, with low attenuation, is present at the input terminal.This represents that the sensor 1220 has been disconnected from thesensor electronics device 1225 or that the sensor is not operatingproperly. If the sensor has been disconnected from the sensorelectronics device 1225, the AC source may be coupled with little or lowattenuation to the input of the detection circuit 1260. As noted above,the detection circuit 1260 may generate an interrupt to themicrocontroller. This interrupt may be received by the microcontrollerand the microcontroller may reduce or eliminate power to one or a numberof components or circuits in the sensor electronics device 1225. Thismay be referred to as the second interrupt. Again, this helps reducepower consumption of the sensor electronics device 1225, specificallywhen the sensor 1220 is not connected to the sensor electronics device1225.

In an alternative embodiment, the AC signal may be applied to thereference electrode 1222, as is illustrated by reference numeral 1291,and an impedance measuring device 1277 may measure the impedance of anarea in the sensor 1220. Illustratively, the area may be an area betweenthe reference electrode and the working electrode, as illustrated bydotted line 1292 in FIG. 12. Under certain operating conditions, theimpedance measuring device 1277 may transmit a signal to the detectioncircuit 1260 if a measured impedance has decreased to below an impedancethreshold or other set criteria. This represents that the sensor issufficiently hydrated. Under other operating conditions, the impedancemeasuring device 1277 may transmit a signal to the detection circuit1260 once the impedance is above an impedance threshold. The detectioncircuit 1260 then transmits the interrupt to the microcontroller 410. Inanother embodiment, the impedance measuring device 1277 may transmit aninterrupt or signal directly to the microcontroller.

In an alternative embodiment, the AC source 1255 may be replaced by a DCsource. If a DC source is utilized, then a resistance measuring elementmay be utilized in place of an impedance measuring element 1277. In anembodiment utilizing the resistance measuring element, once theresistance drops below a resistance threshold or a set criteria, theresistance measuring element may transmit a signal to the detectioncircuit 1260 (represented by dotted line 1293) or directly to themicrocontroller indicating that the sensor is sufficiently hydrated andthat power may be applied to the sensor.

In the embodiment illustrated in FIG. 12, if the detection circuit 1260detects a low level or highly attenuated AC signal from the AC source,an interrupt is generated to the microcontroller 410. This interruptindicates that sensor is sufficiently hydrated. In this embodiment, inresponse to the interrupt, the microcontroller 410 generates a signalthat is transferred to a digital-to-analog converter 420 to instruct orcause the digital-to-analog converter 420 to apply a voltage or currentto the sensor 1220. Any of the different sequence of pulses or shortduration pulses described above in FIG. 6A, 6B, or 6C or the associatedtext describing the application of pulses, may be applied to the sensor1220. Illustratively, the voltage from the DAC 420 may be applied to anop-amp 1275, the output of which is applied to the counter electrode1221 of the sensor 1220. This results in a sensor signal being generatedby the sensor, e.g., the working electrode 1223 of the sensor. Becausethe sensor is sufficiently hydrated, as identified by the interrupt, thesensor signal created at the working electrode 1223 is accuratelymeasuring glucose. The sensor signal is measured by a sensor signalmeasuring device 431 and the sensor signal measuring device 431transmits the sensor signal to the microcontroller 410 where a parameterof a subject's physiological condition is measured. The generation ofthe interrupt represents that a sensor is sufficiently hydrated and thatthe sensor 1220 is now supplying accurate glucose measurements. In thisembodiment, the hydration period may depend on the type and/or themanufacturer of the sensor and on the sensor's reaction to insertion orimplantation in the subject. Illustratively, one sensor 1220 may have ahydration time of five minutes and one sensor 1220 may have a hydrationtime of one minute, two minutes, three minutes, six minutes, or 20minutes. Again, any amount of time may be an acceptable amount ofhydration time for the sensor, but smaller amounts of time arepreferable.

If the sensor 1220 has been connected, but is not sufficiently hydratedor wetted, the effective capacitances C_(r-c) and C_(w-r) may notattenuate the AC signal from the AC source 1255. The electrodes in thesensor 1120 are dry before insertion and because the electrodes are dry,a good electrical path (or conductive path) does not exist between thetwo electrodes. Accordingly, a high level AC signal or lowly attenuatedAC signal may still be detected by the detection circuit 1260 and nointerrupt may be generated. Once the sensor has been inserted, theelectrodes become immersed in the conductive body fluid. This results ina leakage path with lower DC resistance. Also, boundary layer capacitorsform at the metal/fluid interface. In other words, a rather largecapacitance forms between the metal/fluid interface and this largecapacitance looks like two capacitors in series between the electrodesof the sensor. This may be referred to as an effective capacitance. Inpractice, a conductivity of an electrolyte above the electrode is beingmeasured. In some embodiments of the invention, the glucose limitingmembrane (GLM) also illustrates impedance blocking electricalefficiency. An unhydrated GLM results in high impedance, whereas a highmoisture GLM results in low impedance. Low impedance is desired foraccurate sensor measurements.

FIG. 13A illustrates a method of hydrating a sensor according to anembodiment of the inventions herein. In one embodiment, the sensor maybe physically connected 1310 to the sensor electronics device. After theconnection, in one embodiment, a timer or counter may be initiated tocount 1320 a hydration time. After the hydration time has elapsed, asignal may be transmitted 1330 to a subsystem in the sensor electronicsdevice to initiate the application of a voltage to the sensor. Asdiscussed above, in one embodiment, a microcontroller may receive thesignal and instruct the DAC to apply a voltage to the sensor or inanother embodiment of the invention, a switch may receive a signal whichallows a regulator to apply a voltage to the sensor. The hydration timemay be five minutes, two minutes, ten minutes and may vary depending onthe subject and also on the type of sensor.

In an alternative embodiment, after the connection of the sensor to thesensor electronics device, an AC signal (e.g., a low voltage AC signal)may be applied 1340 to the sensor, e.g., the reference electrode of thesensor. The AC signal may be applied because the connection of thesensor to the sensor electronics device allows the AC signal to beapplied to the sensor. After application of the AC signal, an effectivecapacitance forms 1350 between the electrode in the sensor that thevoltage is applied to and the other two electrodes. A detection circuitdetermines 1360 what level of the AC signal is present at the input ofthe detection circuit. If a low level AC signal (or highly attenuated ACsignal) is present at the input of the detection circuit, due to theeffective capacitance forming a good electrical conduit between theelectrodes and the resulting attenuation of the AC signal, an interruptis generated 1370 by the detection circuit and sent to amicrocontroller.

The microcontroller receives the interrupt generated by the detectioncircuit and transmits 1380 a signal to a digital-to-analog converterinstructing or causing the digital-to-analog converter to apply avoltage to an electrode of the sensor, e.g., the counter electrode. Theapplication of the voltage to the electrode of the sensor results in thesensor creating or generating a sensor signal 1390. A sensor signalmeasurement device 431 measures the generated sensor signal andtransmits the sensor signal to the microcontroller. The microcontrollerreceives 1395 the sensor signal from the sensor signal measurementdevice, which is coupled to the working electrode, and processes thesensor signal to extract a measurement of a physiological characteristicof the subject or patient.

FIG. 13B illustrates an additional method for verifying hydration of asensor according to an embodiment of the inventions herein. In theembodiment illustrated in FIG. 13B, the sensor is physically connected1310 to the sensor electronics device. An AC signal is applied 1341 toan electrode, e.g., a reference electrode, in the sensor. Alternatively,in another embodiment, a DC signal is applied 1341 to an electrode inthe sensor. If an AC signal is applied, an impedance measuring elementmeasures 1351 an impedance at a point within the sensor. Alternatively,if a DC signal is applied, a resistance measuring element measures 1351a resistance at a point within the sensor. If the resistance orimpedance is lower than a resistance threshold or an impedancethreshold, respectively, (or other set criteria), then the impedance (orresistance) measuring element transmits 1361 (or allows a signal to betransmitted) to the detection circuit, and the detection circuittransmits an interrupt to the microcontroller identifying that thesensor is hydrated. The reference numbers 1380, 1390, and 1395 are thesame in FIGS. 13A and 13B because they represent the same action.

The microcontroller receives the interrupt and transmits 1380 a signalto a digital-to-analog converter to apply a voltage to the sensor. In analternative embodiment, the digital-to-analog converter can apply acurrent to the sensor, as discussed above. The sensor, e.g., the workingelectrode, creates 1390 a sensor signal, which represents aphysiological parameter of a patient. The microcontroller receives 1395the sensor signal from a sensor signal measuring device, which measuresthe sensor signal at an electrode in the sensor, e.g., the workingelectrode. The microcontroller processes the sensor signal to extract ameasurement of the physiological characteristic of the subject orpatient, e.g., the blood glucose level of the patient.

FIGS. 14A and 14B illustrate methods of combining hydrating of a sensorwith stabilizing of a sensor according to an embodiment of theinventions herein. In an embodiment of the invention illustrated in FIG.14A, the sensor is connected 1405 to the sensor electronics device. TheAC signal is applied 1410 to an electrode of the sensor. The detectioncircuit determines 1420 what level of the AC signal is present at aninput of the detection circuit. If the detection circuit determines thata low level of the AC signal is present at the input (representing ahigh level of attenuation to the AC signal), an interrupt is sent 1430to microcontroller. Once the interrupt is sent to the microcontroller,the microcontroller knows to begin or initiate 1440 a stabilizationsequence, i.e., the application of a number of voltage pulses to anelectrode of the sensors, as described above. For example, themicrocontroller may cause a digital-to-analog converter to apply threevoltage pulses (having a magnitude of +0.535 volts) to the sensor witheach of the three voltage pulses followed by a period of three voltagepulses (having a magnitude of 1.07 volts to be applied). This may bereferred to transmitting a stabilization sequence of voltages. Themicrocontroller may cause this by the execution of a software program ina read-only memory (ROM) or a random access memory. After thestabilization sequence has finished executing, the sensor may generate1450 a sensor signal, which is measured and transmitted to amicrocontroller.

The detection circuit may determine 1432 that a high level AC signal hascontinued to be present at the input of the detection circuit (e.g., aninput of a comparator), even after a hydration time threshold haselapsed. For example, the hydration time threshold may be 10 minutes.After 10 minutes has elapsed, the detection circuit may still bedetecting that a high level AC signal is present. At this point in time,the detection circuit may transmit 1434 a hydration assist signal to themicrocontroller. If the microcontroller receives the hydration assistsignal, the microcontroller may transmit 1436 a signal to cause a DAC toapply a voltage pulse or a series of voltage pulses to assist the sensorin hydration. In one embodiment, the microcontroller may transmit asignal to cause the DAC to apply a portion of the stabilization sequenceor other voltage pulses to assist in hydrating the sensor. In thisembodiment, the application of voltage pulses may result in the lowlevel AC signal (or highly attenuated signal) being detected 1438 at thedetection circuit. At this point, the detection circuit may transmit aninterrupt, as is disclosed in step 1430, and the microcontroller mayinitiate a stabilization sequence.

FIG. 14B illustrates a second embodiment of a combination of a hydrationmethod and a stabilization method where feedback is utilized in thestabilization process. A sensor is connected 1405 to a sensorelectronics device. An AC signal (or a DC signal) is applied 1411 to thesensor. In an embodiment, the AC signal (or the DC signal) is applied toan electrode of the sensor, e.g. the reference electrode. An impedancemeasuring device (or resistance measuring device) measures 1416 theimpedance (or resistance) within a specified area of the sensor, e.g.,between the reference electrode and the working electrode. The measuredimpedance (or resistance) may be compared 1421 to an impedance orresistance value to see if the impedance (or resistance) is low enoughin the sensor, which indicates the sensor is hydrated. If the impedance(or resistance) is below the impedance (or resistance) value or otherset criteria, (which may be a threshold value), an interrupt istransmitted 1431 to the microcontroller. After receiving the interrupt,the microcontroller transmits 1440 a signal to the DAC instructing theDAC to apply a stabilization sequence of voltages (or currents) to thesensor. After the stabilization sequence has been applied to the sensor,a sensor signal is created in the sensor (e.g., at the workingelectrode), is measured by a sensor signal measuring device, istransmitted by the sensor signal measuring device, and is received 1450by the microcontroller. Because the sensor is hydrated and thestabilization sequence of voltages has been applied to the sensor, thesensor signal is accurately measuring a physiological parameter (i.e.,blood glucose).

FIG. 14C illustrates a third embodiment in which a stabilization methodand hydration method are combined. In this embodiment, the sensor isconnected 1500 to the sensor electronics device. After the sensor isphysically connected to the sensor electronics device, an AC signal (orDC signal) is applied 1510 to an electrode (e.g., reference electrode)of the sensor. At the same time, or around the same time, themicrocontroller transmits a signal to cause the DAC to apply 1520 astabilization voltage sequence to the sensor. In an alternativeembodiment, a stabilization current sequence may be applied to thesensor instead of a stabilization voltage sequence. The detectioncircuit determines 1530 what level of an AC signal (or DC signal) ispresent at an input terminal of the detection circuit. If there is a lowlevel AC signal (or DC signal), representing a highly attenuated ACsignal (or DC signal), present at the input terminal of the detectioncircuit, an interrupt is transmitted 1540 to the microcontroller.Because the microcontroller has already initiated the stabilizationsequence, the microcontroller receives the interrupt and sets 1550 afirst indicator that the sensor is sufficiently hydrated. After thestabilization sequence is complete, the microcontroller sets 1555 asecond indicator indicating the completion of the stabilizationsequence. The application of the stabilization sequence voltages resultsin the sensor, e.g., the working electrode, creating 1560 a sensorsignal, which is measured by a sensor signal measuring circuit, and sentto the microcontroller. If the second indicator that the stabilizationsequence is complete is set and the first indicator that the hydrationis complete is set, the microcontroller is able to utilize 1570 thesensor signal. If one or both of the indicators are not set, themicrocontroller may not utilize the sensor signal because the sensorsignal may not represent accurate measurements of the physiologicalmeasurements of the subject.

The above-described hydration and stabilization processes may be used,in general, as part of a larger continuous glucose monitoring (CGM)methodology. The current state of the art in continuous glucosemonitoring is largely adjunctive, meaning that the readings provided bya CGM device (including, e.g., an implantable or subcutaneous sensor)cannot be used without a reference value in order to make a clinicaldecision. The reference value, in turn, must generally be obtained froma finger stick using, e.g., a BG meter. The reference value is neededbecause there is a limited amount of information that is available fromthe sensor/sensing component. Specifically, only the raw sensor value(i.e., the sensor current or Isig) and the counter voltage, which is thevoltage between the counter electrode and the reference electrode (see,e.g., FIG. 5), may be provided by the sensing component for processing.Therefore, during analysis, if it appears that the raw sensor signal isabnormal (e.g., if the signal is decreasing), the only way one candistinguish between a sensor failure and a physiological change withinthe user/patient (i.e., glucose level changing in the body) may be byacquiring a reference glucose value via a finger stick. As is known, thereference finger stick is also used for calibrating the sensor.

Embodiments of the inventions described herein are directed toadvancements and improvements in continuous glucose monitoring resultingin a more autonomous system, as well as related devices andmethodologies, wherein the requirement of reference finger sticks may beminimized, or eliminated, and whereby clinical decisions may be madebased on information derived from the sensor signal(s) alone, with ahigh level of reliability. From a sensor-design standpoint, inaccordance with embodiments of the present inventions, such autonomy maybe achieved through electrode redundancy, sensor redundancy (including,e.g., complex redundancy between two or more sensors), sensordiagnostics, and Isig and/or sensor glucose (SG) fusion.

In the discussion herein, and for purposes of the instant inventions,“redundancy” refers to the existence/use of two or more electrodes,whether contained on/within a single probe (or “flex”), or containedon/within two or more flexes, and “complex redundancy” refers to theexistence/use of two (or more) sensors where (at least) two of thesensors are not identical. Thus, “redundant” electrodes may be containedon/within a single flex, on/within two or more flex(es) that areidentical, or on/within two or more flex(es) that are not identical. Aswill be explored further hereinbelow, redundancy may be achieved, e.g.,through the use of multiple working electrodes to produce multiplesignals indicative of the patient's blood glucose (BG) level. Themultiple signals, in turn, may be used to generate a fused glucosevalue, as well as to assess the relative health of the (working)electrodes, the overall reliability of the sensor, and the frequency ofthe need, if at all, for calibration reference values.

For example, it is known that acquiring signals from multipleelectrochemical sensors can provide improved performance in the form ofsimple redundancy, accomplished through either multiple electrodes onthe same probe (or flex), or by utilizing spatial separation and twoseparate probes. Medtronic, Inc., for example, sells hospital glucosesensors that include two probes, with two working electrodes on eachprobe, resulting in four independent glucose signals.

In contrast with simple redundancy, orthogonal redundancy may be definedas two devices employing two different technologies to reach the samegoal, where the failure modes of the two devices are completely uniqueand do not intersect. Thus, orthogonal redundancy may be created bycombining, e.g., the technologies of optical sensing and electrochemicalsensing. Clearly, an advantage of orthogonal redundancy is that the twotypes of sensors—e.g., optical and electrochemical (or “echem”)sensors—are subject to different types of interferences, failure modes,and body responses. On the other hand, the use of two completelydifferent technologies introduces additional layers of design andcomputational complexity to the measurement and analysis of glucoselevels within a patient's body.

Pseudo-orthogonal redundancy, on the other hand, may be achieved byutilizing the same technology, but with variations, so as to generatecomplementary glucose measurements while minimizing additional designand/or computational complexities. For example, two or moreelectrochemical sensors may be employed, wherein one (or more) sensor(s)may be a traditional peroxide-based sensor, and one (or more) sensor(s)may measure glucose through computing differences in oxygen between twoworking electrodes (usually on the same sensor).

In yet another specific type of redundancy, as will be explored in moredetail hereinbelow, in embodiments of the inventions herein, a sensorsystem employing complex redundancy may include two (or more) sensors,of which (at least) two sensors are dissimilar to one another in design(and may also employ different chemistry and/or size). Here, one (ormore) of the sensors may be designed to have, e.g., considerably betterhydration and/or stabilization characteristics, but may not last past 2or 3 days. The other sensor(s), on the other hand, may have long-lastingdurability, but slow initial hydration and/or stabilization. In such acase, an algorithm may be designed whereby the first sensor(s) is usedto generate glucose data during early wear, after which the firstsensor(s) may be used to calibrate the second sensor(s), and then aswitch-over may be made to the second sensor(s) for generating glucosedata during the remainder of the life of the glucose sensor system.

Sensor diagnostics includes the use of additional (diagnostic)information which can provide a real-time insight into the health of thesensor. In this regard, it has been discovered that ElectrochemicalImpedance Spectroscopy (EIS) provides such additional information in theform of sensor impedance and impedance-related parameters at differentfrequencies. Moreover, advantageously, it has been further discoveredthat, for certain ranges of frequencies, impedance and/orimpedance-related data are substantially glucose independent. Suchglucose independence enables the use of a variety of EIS-based markersor indicators for not only producing a robust, highly-reliable sensorglucose value (through fusion methodologies, to be described in moredetail hereinbelow), but also assessing the condition, health, age, andefficiency of individual electrode(s) and of the overall sensor(s)substantially independently of the glucose-dependent Isig.

For example, analysis of the glucose-independent impedance data providesinformation on the efficiency of the sensor with respect to how quicklyit hydrates and is ready for data acquisition using, e.g., values for 1kHz real-impedance, 1 kHz imaginary impedance, and Nyquist Slope (to bedescribed in more detail hereinbelow). Moreover, glucose-independentimpedance data provides information on potential occlusion(s) that mayexist on the sensor membrane surface, which occlusion(s) may temporarilyblock passage of glucose into the sensor and thus cause the signal todip (using, e.g., values for 1 kHz real impedance). In addition,glucose-independent impedance data provides information on loss ofsensor sensitivity during extended wear—potentially due to local oxygendeficit at the insertion site—using, e.g., values for phase angle and/orimaginary impedance at 1 kHz and higher frequencies.

Within the context of (electrode) redundancy and EIS, a fusion algorithmmay be used to take the diagnostic information provided by EIS for eachredundant electrode and assess the reliability of each electrodeindependently. Weights, which are a measure of reliability, may then beadded for each independent signal, and a single fused signal may becalculated that can be used to generate sensor glucose values as seen bythe patient/subject. As can be seen from the foregoing, the combined useof redundancy, sensor diagnostics using EIS, and EIS-based fusionalgorithms allows for a more reliable overall CGM system. In addition,EIS diagnostics scrutinize the health of each electrode autonomouslywithout the need for a reference glucose value (finger stick), therebyreducing the number of reference values required.

EIS, or AC impedance methods, study the system response to theapplication of a periodic small amplitude AC signal. This is shownillustratively in FIG. 15A, where E is the applied potential, I is thecurrent, and impedance (Z) is defined as ΔE/ΔI. However, althoughimpedance, per se, may be mathematically simply defined as ΔE/ΔI,heretofore, there has been no commercialization success in applicationof EIS technology to continuous glucose monitoring. This has been due,in part, to the fact that glucose sensors are very complicated systemsand, so far, no mathematical models have been developed which cancompletely explain the complexity of the EIS output for a glucosesensor.

One simplified electrical circuit model that has been used to describeelectrochemical impedance spectroscopy is shown in FIG. 15B. In thisillustration, IHP stands for Inner Helmholtz Plane, OHP stands for OuterHelmholtz Plane, CE is the counter electrode, WE is the workingelectrode, C_(d) is double layer capacitance, R_(p) is polarizationresistance, Z_(w) is Warburg impedance, and R_(s) is solutionresistance. Each of the latter four components—double layer capacitance(C_(d)), Warburg impedance (Z_(w)), polarization resistance (R_(p)), andsolution resistance (R_(s))—may play a significant role in sensorperformance, and can be measured separately by applying low- orhigh-frequency alternating working potential. For example, Warburgimpedance is closely related to diffusional impedance of electrochemicalsystems—which is primarily a low-frequency impedance—and, as such,exists in all diffusion-limited electrochemical sensors. Thus, bycorrelating one or more of these components with one or more componentsand/or layers of a glucose sensor, one may use EIS technology as asensor-diagnostics tool.

As is known, impedance may be defined in terms of its magnitude andphase, where the magnitude (|Z|) is the ratio of the voltage differenceamplitude to the current amplitude, and the phase (θ) is the phase shiftby which the current is ahead of the voltage. When a circuit is drivensolely with direct current (DC), the impedance is the same as theresistance, i.e., resistance is a special case of impedance with zerophase angle. However, as a complex quantity, impedance may also berepresented by its real and imaginary parts. In this regard, the realand imaginary impedance can be derived from the impedance magnitude andphase using the following equations:

Real Impedance(ω)=Magnitude(ω)×cos(Phase(ω)/180×π)

Imaginary Impedance(ω)=Magnitude(ω)×sin(Phase(ω)/180×π)

where ω represents the input frequency at which the magnitude (in ohms)and the phase (in degrees) are measured. The relationship betweenimpedance, on the one hand, and current and voltage on theother—including how the former may be calculated based on measurement ofthe latter—will be explored more fully below in connection with thesensor electronics, including the Application Specific IntegratedCircuit (ASIC), that has been developed for use in embodiments of theinventions described herein.

Continuing with the circuit model shown in FIG. 15B, total systemimpedance may be simplified as:

${Z_{t}(\omega)} = {{Z_{w}(\omega)} + R_{s} + \frac{R_{p}}{1 + {\omega^{2}R_{p}^{2}C_{d}^{2}}} - {j\frac{{\omega R}_{p}^{2}C_{d}}{1 + {\omega^{2}R_{p}^{2}C_{d}^{2}}}}}$

where Z_(w)(ω) is the Warburg impedance, ω is the angular velocity, j isthe imaginary unit (used instead of the traditional “i” so as not to beconfused with electric current), and C_(d), R_(p), and R_(s) are thedouble layer capacitance, the polarization resistance, and the solutionresistance, respectively (as defined previously). Warburg impedance canbe calculated as

${Z_{w}(\omega)} = {Z_{0}\frac{\tanh \left( ({js})^{m} \right)}{({js})^{m}}}$$s = {\frac{L^{2}}{\omega/D} = \left( \frac{{Membrane}\mspace{14mu} {Trickness}}{{Frequency}\mspace{14mu} {Dependent}\mspace{14mu} {Diffusion}\mspace{14mu} {Length}} \right)^{2}}$$Z_{0} = \frac{RTL}{n^{2}F^{2}{DC}}$

where D is diffusivity, L is the sensor membrane thickness, C isPeroxide concentration, and m: ½ corresponds to a 45° Nyquist slope.

A Nyquist plot is a graphical representation, wherein the real part ofimpedance (Real Z) is plotted against its imaginary part (Img Z) acrossa spectrum of frequencies. FIG. 16A shows a generalized example of aNyquist Plot, where the X value is the real part of the impedance andthe Y value is the imaginary part of the impedance. The phase angle isthe angle between the impedance point (X,Y)—which defines a vectorhaving magnitude |Z|—and the X axis.

The Nyquist plot of FIG. 16A is generated by applying AC voltages plus aDC voltage (DC bias) between the working electrode and the counterelectrode at selected frequencies from 0.1 Hz to 1000 MHz (i.e., afrequency sweep). Starting from the right, the frequency increases from0.1 Hz. With each frequency, the real and imaginary impedance can becalculated and plotted. As shown, a typical Nyquist plot of anelectrochemical system may look like a semicircle joined with a straightline at an inflection point, wherein the semicircle and the lineindicate the plotted impedance. In certain embodiments, the impedance atthe inflection point is of particular interest since it is easiest toidentify in the Nyquist plot and may define an intercept. Typically, theinflection point is close to the X axis, and the X value of theinflection point approximates the sum of the polarization resistance andsolution resistance (R_(p)+R_(s)).

With reference to FIG. 16B, a Nyquist plot may typically be described interms of a lower-frequency region 1610 and a higher-frequency region1620, where the labels “higher frequency” and “lower frequency” are usedin a relative sense, and are not meant to be limiting. Thus, forexample, the lower-frequency region 1610 may illustratively include datapoints obtained for a frequency range between about 0.1 Hz and about 100Hz (or higher), and the higher-frequency region 1620 may illustrativelyinclude data points obtained for a frequency range between about 1 kHz(or lower) and about 8 kHz (and higher). In the lower-frequency region1610, the Nyquist slope represents the gradient of the linear fit 1630of the lower-frequency data points in the Nyquist plot. As shown, in thehigher-frequencies region 1620, the value of imaginary impedance isminimal, and may become negligible. As such, the intercept 1600 isessentially the value of the real impedance at the higher frequencies(e.g., approximately in the 1 kHz to 8 kHz range in this case). In FIG.16B, the intercept 1600 is at about 25 kOhms.

FIGS. 16C and 16D demonstrate how a glucose sensor responds to asinusoidal (i.e., alternating) working potential. In these figures, GLMis the sensor's glucose limiting membrane, AP is the adhesion promoter,HSA is human serum albumin, GOX is glucose oxidase enzyme (layer),E_(dc) is DC potential, E_(ac) is AC potential, and C_(peroxtae)′ isperoxide concentration during AC application. As shown in FIG. 16C, ifthe sensor diffusion length, which is a function of AC potentialfrequency, molecular diffusivity, and membrane thickness, is smallcompared to the membrane (GOX) length, the system gives a relativelylinear response with a constant phase angle (i.e., infinite). Incontrast, if the diffusion length is equal to the membrane (GOX) length,the system response will become finite, resulting in a semi-circleNyquist plot, as shown in FIG. 16D. The latter usually holds true forlow-frequency EIS, where the non-Faradaic process is negligible.

In performing an EIS analysis, an AC voltage of various frequencies anda DC bias may be applied between, e.g., the working and referenceelectrodes. In this regard, EIS is an improvement over previousmethodologies that may have limited the application to a simple DCcurrent or an AC voltage of single frequency. Although, generally, EISmay be performed at frequencies in the μHz to MHz range, in embodimentsof the inventions described herein, a narrower range of frequencies(e.g., between about 0.1 Hz and about 8 kHz) may be sufficient. Thus, insome embodiments, AC potentials may be applied that fall within afrequency range of between about 0.1 Hz and about 8 kHz, with aprogrammable amplitude of up to at least 100 mV, and preferably at about50 mV.

Within the above-mentioned frequency range, the relatively-higherfrequencies—i.e., those that fall generally between about 1 kHz andabout 8 kHz—are used to scrutinize the capacitive nature of the sensor.Depending on the thickness and permeability of membranes, a typicalrange of impedance at the relatively-higher frequencies may be, e.g.,between about 500 Ohms and 25 kOhms, and a typical range for the phasemay be, e.g., between 0 degrees and −40 degrees. The relatively-lowerfrequencies—i.e., those that fall generally between about 0.1 Hz andabout 100 Hz—on the other hand, are used to scrutinize the resistivenature of the sensor. Here, depending on electrode design and the extentof metallization, a typical functioning range for output real impedancemay be, e.g., between about 50 kOhms and 300 kOhms, and a typical rangefor the phase may be between about −50 degrees to about −90 degrees. Theabove illustrative ranges are shown, e.g., in the Bode plots of FIGS.16E and 16F.

As noted previously, the phrases “higher frequencies” and “lowerfrequencies” are meant to be used relative to one another, rather thanin an absolute sense, and they, as well as the typical impedance andphase ranges mentioned above, are meant to be illustrative, and notlimiting. Nevertheless, the underlying principle remains the same: thecapacitive and resistive behavior of a sensor can be scrutinized byanalyzing the impedance data across a frequency spectrum, wherein,typically, the lower frequencies provide information about the moreresistive components (e.g., the electrode, etc.), while the higherfrequencies provide information about the capacitive components (e.g.,membranes). However, the actual frequency range in each case isdependent on the overall design, including, e.g., the type(s) ofelectrode(s), the surface area of the electrode(s), membrane thickness,the permeability of the membrane, and the like. See also FIG. 15Bregarding general correspondence between high-frequency circuitcomponents and the sensor membrane, as well as between low-frequencycircuit components and the Faradaic process, including, e.g., theelectrode(s).

EIS may be used in sensor systems where the sensor includes a singleworking electrode, as well those in which the sensor includes multiple(redundant) working electrodes. In one embodiment, EIS provides valuableinformation regarding the age (or aging) of the sensor. Specifically, atdifferent frequencies, the magnitude and the phase angle of theimpedance vary. As seen in FIG. 17, the sensor impedance—in particular,the sum of Rp and Rs—reflects the sensor age as well as the sensor'soperating conditions. Thus, a new sensor normally has higher impedancethan a used sensor as seen from the different plots in FIG. 17. In thisway, by considering the X-value of the sum of Rp and Rs, a threshold canbe used to determine when the sensor's age has exceeded the specifiedoperating life of the sensor. It is noted that, although for theillustrative examples shown in FIGS. 17-21 and discussed below, thevalue of real impedance at the inflection point (i.e., Rp+Rs) is used todetermine the aging, status, stabilization, and hydration of the sensor,alternative embodiments may use other EIS-based parameters, such as,e.g., imaginary impedance, phase angle, Nyquist slope, etc. in additionto, or in place of, real impedance.

FIG. 17 illustrates an example of a Nyquist plot over the life time of asensor. The points indicated by arrows are the respective inflectionpoints for each of the sweeps across the frequency spectrum. Forexample, before initialization (at time t=0), Rs+Rp is higher than 8.5kOhms, and after initialization (at time t=0.5 hr), the value of Rs+Rpdropped to below 8 kOhms. Over the next six days, Rs+Rp continues todecrease, such that, at the end of the specified sensor life, Rs+Rpdropped to below 6.5 kOhms. Based on such examples, a threshold valuecan be set to specify when the Rs+Rp value would indicate the end of thespecified operating life of the sensor. Therefore, the EIS techniqueallows closure of the loophole of allowing a sensor to be re-used beyondthe specified operating time. In other words, if the patient attempts tore-use a sensor after the sensor has reached its specified operatingtime by disconnecting and then re-connecting the sensor again, the EISwill measure abnormally-low impedance, thereby enabling the system toreject the sensor and prompt the patient for a new sensor.

Additionally, EIS may enable detection of sensor failure by detectingwhen the sensor's impedance drops below a low impedance threshold levelindicating that the sensor may be too worn to operate normally. Thesystem may then terminate the sensor before the specified operatinglife. As will be explored in more detail below, sensor impedance canalso be used to detect other sensor failure (modes). For example, when asensor goes into a low-current state (i.e., sensor failure) due to anyvariety of reasons, the sensor impedance may also increase beyond acertain high impedance threshold. If the impedance becomes abnormallyhigh during sensor operation, due, e.g., to protein or polypeptidefouling, macrophage attachment or any other factor, the system may alsoterminate the sensor before the specified sensor operating life.

FIG. 18 illustrates how the EIS technique can be applied during sensorstabilization and in detecting the age of the sensor in accordance withcertain embodiments. The logic of FIG. 18 begins at 1800 after thehydration procedure and sensor initialization procedure describedpreviously has been completed. In other words, the sensor has beendeemed to be sufficiently hydrated, and the first initializationprocedure has been applied to initialize the sensor. The initializationprocedure may preferably be in the form of voltage pulses as describedpreviously in the detailed description. However, in alternativeembodiments, different waveforms can be used for the initializationprocedure. For example, a sine wave can be used, instead of the pulses,to accelerate the wetting or conditioning of the sensor. In addition, itmay be necessary for some portion of the waveform to be greater than thenormal operating voltage of the sensor, i.e., 0.535 volt.

At block 1810, an EIS procedure is applied and the impedance is comparedto both a first high and a first low threshold. An example of a firsthigh and first low threshold value would be 7 kOhms and 8.5 kOhms,respectively, although the values can be set higher or lower as needed.If the impedance, for example, Rp+Rs, is higher than the first highthreshold, the sensor undergoes an additional initialization procedure(e.g., the application of one or more additional pulses) at block 1820.Ideally, the number of total initialization procedures applied toinitialize the sensor would be optimized to limit the impact on both thebattery life of the sensor and the overall amount of time needed tostabilize a sensor. Thus, by applying EIS, fewer initializations can beinitially performed, and the number of initializations can beincrementally added to give just the right amount of initializations toready the sensor for use. Similarly, in an alternative embodiment, EIScan be applied to the hydration procedure to minimize the number ofinitializations needed to aid the hydration process as described inFIGS. 13-14.

On the other hand, if the impedance, for example, Rp+Rs, is below thefirst low threshold, the sensor will be determined to be faulty andwould be terminated immediately at block 1860. A message will be givento the user to replace the sensor and to begin the hydration processagain. If the impedance is within the high and low thresholds, thesensor will begin to operate normally at block 1830. The logic thanproceeds to block 1840 where an additional EIS is performed to check theage of the sensor. The first time the logic reaches block 1840, themicrocontroller will perform an EIS to gauge the age of the sensor toclose the loophole of the user being able to plug in and plug out thesame sensor. In future iterations of the EIS procedure as the logicreturns to block 1840, the microprocessor will perform an EIS at fixedintervals during the specified life of the sensor. In one preferredembodiment, the fixed interval is set for every 2 hours, however, longeror shorter periods of time can easily be used.

At block 1850, the impedance is compared to a second set of high and lowthresholds. An example of such second high and low threshold values maybe 5.5 kOhms and 8.5 kOhms, respectively, although the values can be sethigher or lower as needed. As long as the impedance values stay within asecond high and low threshold, the logic proceeds to block 1830, wherethe sensor operates normally until the specified sensor life, forexample, 5 days, is reached. Of course, as described with respect toblock 1840, EIS will be performed at the regularly scheduled intervalsthroughout the specified sensor life. However, if, after the EIS isperformed, the impedance is determined to have dropped below a secondlower threshold or risen above a second higher threshold at block 1850,the sensor is terminated at block 1860. In further alternativeembodiments, a secondary check can be implemented of a faulty sensorreading. For example, if the EIS indicates that the impedance is out ofthe range of the second high and low thresholds, the logic can perform asecond EIS to confirm that the second set of thresholds is indeed notmet (and confirm that the first EIS was correctly performed) beforedetermining the end of sensor at block 1860.

FIG. 19 builds upon the above description and details a possibleschedule for performing diagnostic EIS procedures. Each diagnostic EISprocedure is optional and it is possible to not schedule any diagnosticEIS procedure or to have any combination of one or more diagnostic EISprocedures, as deemed needed. The schedule of FIG. 19 begins at sensorinsertion at point 1900. Following sensor insertion, the sensorundergoes a hydration period 1910. This hydration period is importantbecause a sensor that is not sufficiently hydrated may give the userinaccurate readings, as described previously. The first optionaldiagnostic EIS procedure at point 1920 is scheduled during thishydration period 1910 to ensure that the sensor is sufficientlyhydrated. The first diagnostic EIS procedure 1920 measures the sensorimpedance value to determine if the sensor has been sufficientlyhydrated. If the first diagnostic EIS procedure 1920 determinesimpedance is within a set high and low threshold, indicating sufficienthydration, the sensor controller will allow the sensor power-up at point1930. Conversely, if the first diagnostic EIS procedure 1920 determinesimpedance is outside a set high and low threshold, indicatinginsufficient hydration, the sensor hydration period 1910 may beprolonged. After prolonged hydration, once a certain capacitance hasbeen reached between the sensor's electrodes, meaning the sensor issufficiently hydrated, power-up at point 1930 can occur.

A second optional diagnostic EIS procedure 1940 is scheduled aftersensor power-up at point 1930, but before sensor initialization startsat point 1950. Scheduled here, the second diagnostic EIS procedure 1940can detect if a sensor is being re-used prior to the start ofinitialization at 1950. The test to determine if the sensor is beingreused was detailed in the description of FIG. 18. However, unlike theprevious description with respect to FIG. 18, where the aging test isperformed after initialization is completed, the aging test is shown inFIG. 19 as being performed before initialization. It is important toappreciate that the timeline of EIS procedures described in FIG. 19 canbe rearranged without affecting the overall teaching of the application,and that the order of some of the steps can be interchanged. Asexplained previously, the second diagnostic EIS procedure 1940 detects are-used sensor by determining the sensor's impedance value and thencomparing it to a set high and low threshold. If impedance falls outsideof the set threshold, indicating the sensor is being re-used, the sensormay then be rejected and the user prompted to replace it with a newsensor. This prevents the complications that may arise out of re-use ofan old sensor. Conversely, if impedance falls within a set threshold,sensor initialization 1950 can start with the confidence that a newsensor is being used.

A third optional diagnostic EIS procedure 1960 is scheduled afterinitialization starts at point 1950. The third diagnostic EIS procedure1960 tests the sensor's impedance value to determine if the sensor isfully initialized. The third diagnostic EIS procedure 1960 should beperformed at the minimum amount of time needed for any sensor to befully initialized. When performed at this time, sensor life is maximizedby limiting the time a fully initialized sensor goes unused, andover-initialization is averted by confirming full initialization of thesensor before too much initialization occurs. Preventingover-initialization is important because over-initialization results ina suppressed current which can cause inaccurate readings. However,under-initialization is also a problem, so if the third diagnostic EISprocedure 1960 indicates the sensor is under-initialized, an optionalinitialization at point 1970 may be performed in order to fullyinitialize the sensor. Under-initialization is disadvantageous becausean excessive current results that does not relate to the actual glucoseconcentration. Because of the danger of under- and over-initialization,the third diagnostic EIS procedure plays an important role in ensuringthe sensor functions properly when used.

In addition, optional periodic diagnostic EIS procedures 1980 can bescheduled for the time after the sensor is fully initialized. The EISprocedures 1980 can be scheduled at any set interval. As will bediscussed in more detail below, EIS procedures 1980 may also betriggered by other sensor signals, such as an abnormal current or anabnormal counter electrode voltage. Additionally, as few or as many EISprocedures 1980 can be scheduled as desired. In preferred embodiments,the EIS procedure used during the hydration process, sensor life check,initialization process, or the periodic diagnostic tests is the sameprocedure. In alternative embodiments, the EIS procedure can beshortened or lengthened (i.e., fewer or more ranges of frequencieschecked) for the various EIS procedures depending on the need to focuson specific impedance ranges. The periodic diagnostic EIS procedures1980 monitor impedance values to ensure that the sensor is continuing tooperate at an optimal level.

The sensor may not be operating at an optimal level if the sensorcurrent has dropped due to polluting species, sensor age, or acombination of polluting species and sensor age. A sensor that has agedbeyond a certain length is no longer useful, but a sensor that has beenhampered by polluting species can possibly be repaired. Pollutingspecies can reduce the surface area of the electrode or the diffusionpathways of analytes and reaction byproducts, thereby causing the sensorcurrent to drop. These polluting species are charged and graduallygather on the electrode or membrane surface under a certain voltage.Previously, polluting species would destroy the usefulness of a sensor.Now, if periodic diagnostic EIS procedures 1980 detect impedance valueswhich indicate the presence of polluting species, remedial action can betaken. When remedial action is to be taken is described with respect toFIG. 20. Periodic diagnostic EIS procedures 1980 therefore becomeextremely useful because they can trigger sensor remedial action whichcan possibly restore the sensor current to a normal level and prolongthe life of the sensor. Two possible embodiments of sensor remedialactions are described below in the descriptions of FIGS. 21A and 21B.

Additionally, any scheduled diagnostic EIS procedure 1980 may besuspended or rescheduled when certain events are determined imminent.Such events may include any circumstance requiring the patient to checkthe sensor reading, including for example when a patient measures his orher BG level using a test strip meter in order to calibrate the sensor,when a patient is alerted to a calibration error and the need to measurehis or her BG level using a test strip meter a second time, or when ahyperglycemic or hypoglycemic alert has been issued but notacknowledged.

FIG. 20 illustrates a method of combining diagnostic EIS procedures withsensor remedial action. The block 2000 diagnostic procedure may be anyof the periodic diagnostic EIS procedures 1980 as detailed in FIG. 19.The logic of this method begins when a diagnostic EIS procedure isperformed at block 2000 in order to detect the sensor's impedance value.As noted, in specific embodiments, the EIS procedure applies acombination of a DC bias and an AC voltage of varying frequencieswherein the impedance detected by performing the EIS procedure is mappedon a Nyquist plot, and an inflection point in the Nyquist plotapproximates a sum of polarization resistance and solution resistance(i.e., the real impedance value). After the block 2000 diagnostic EISprocedure detects the sensor's impedance value, the logic moves to block2010.

At block 2010, the impedance value is compared to a set high and lowthreshold to determine if it is normal. If impedance is within the setboundaries of the high and low thresholds at block 2010, normal sensoroperation is resumed at block 2020 and the logic of FIG. 20 will enduntil a time when another diagnostic EIS procedure is scheduled.Conversely, if impedance is determined to be abnormal (i.e., outside theset boundaries of the high and low thresholds) at block 2010, remedialaction at block 2030 is triggered. An example of a high and lowthreshold value that would be acceptable during a sensor life would be5.5 kOhms and 8.5 kOhms, respectively, although the values can be sethigher or lower as needed.

The block 2030 remedial action is performed to remove any of thepolluting species, which may have caused the abnormal impedance value.In preferred embodiments, the remedial action is performed by applying areverse current, or a reverse voltage between the working electrode andthe reference electrode. The specifics of the remedial action will bedescribed in more detail with respect to FIG. 21. After the remedialaction is performed at block 2030, impedance value is again tested by adiagnostic EIS procedure at block 2040. The success of the remedialaction is then determined at block 2050 when the impedance value fromthe block 2040 diagnostic EIS procedure is compared to the set high orlow threshold. As in block 2010, if impedance is within the setthresholds, it is deemed normal, and if impedance is outside the setthresholds, it is deemed abnormal.

If the sensor's impedance value is determined to have been restored tonormal at block 2050, normal sensor operation at block 2020 will occur.If impedance is still not normal, indicating that either sensor age isthe cause of the abnormal impedance or the remedial action wasunsuccessful in removing the polluting species, the sensor is thenterminated at block 2060. In alternative embodiments, instead ofimmediately terminating the sensor, the sensor may generate a sensormessage initially requesting the user to wait and then perform furtherremedial action after a set period of time has elapsed. This alternativestep may be coupled with a separate logic to determine if the impedancevalues are getting closer to being within the boundary of the high andlow threshold after the initial remedial action is performed. Forexample, if no change is found in the sensor impedance values, thesensor may then decide to terminate. However, if the sensor impedancevalues are getting closer to the preset boundary, yet still outside theboundary after the initial remedial action, an additional remedialaction could be performed. In yet another alternative embodiment, thesensor may generate a message requesting the user to calibrate thesensor by taking a finger stick meter measurement to further confirmwhether the sensor is truly failing. All of the above embodiments workto prevent a user from using a faulty sensor that produces inaccuratereadings.

FIG. 21A illustrates one embodiment of the sensor remedial actionpreviously mentioned. In this embodiment, blockage created by pollutingspecies is removed by reversing the voltage being applied to the sensorbetween the working electrode and the reference electrode. The reversedDC voltage lifts the charged, polluting species from the electrode ormembrane surface, clearing diffusion pathways. With cleared pathways,the sensor's current returns to a normal level and the sensor can giveaccurate readings. Thus, the remedial action saves the user the time andmoney associated with replacing an otherwise effective sensor.

FIG. 21B illustrates an alternative embodiment of the sensor remedialaction previously mentioned. In this embodiment, the reversed DC voltageapplied between the working electrode and the reference electrode iscoupled with an AC voltage. By adding the AC voltage, certain tightlyabsorbed species or species on the superficial layer can be removedsince the AC voltage can extend its force further from the electrode andpenetrate all layers of the sensor. The AC voltage can come in anynumber of different waveforms. Some examples of waveforms that could beused include square waves, triangular waves, sine waves, or pulses. Aswith the previous embodiment, once polluting species are cleared, thesensor can return to normal operation, and both sensor life and accuracyare improved.

While the above examples illustrate the use, primarily, of realimpedance data in sensor diagnostics, embodiments of the inventionsdescribed herein are also directed to the use of other EIS-based, andsubstantially analyte-independent, parameters (in addition to realimpedance) in sensor diagnostic procedures. For example, as mentionedpreviously, analysis of (substantially) glucose-independent impedancedata, such as, e.g., values for 1 kHz real-impedance and 1 kHz imaginaryimpedance, as well as Nyquist slope, provide information on theefficiency of the sensor with respect to how quickly it hydrates and isready for data acquisition. Moreover, (substantially)glucose-independent impedance data, such as, e.g., values for 1 kHz realimpedance, provides information on potential occlusion(s) that may existon the sensor membrane surface, which occlusion(s) may temporarily blockpassage of glucose into the sensor and thus cause the signal to dip.

In addition, (substantially) glucose-independent impedance data, suchas, e.g., values for higher-frequency phase angle and/or imaginaryimpedance at 1 kHz and higher frequencies, provides information on lossof sensor sensitivity during extended wear, which sensitivity loss maypotentially be due to local oxygen deficit at the insertion site. Inthis regard, the underlying mechanism for oxygen deficiency-ledsensitivity loss may be described as follows: when local oxygen isdeficient, sensor output (i.e., Isig and SG) will be dependent on oxygenrather than glucose and, as such, the sensor will lose sensitivity toglucose. Other markers, including 0.1 Hz real impedance, the counterelectrode voltage (Vcntr), and EIS-induced spikes in the Isig may alsobe used for the detection of oxygen deficiency-led sensitivity loss.Moreover, in a sensor system with redundant electrodes, the relativedifferences in 1 kHz real impedance, 1 kHz imaginary impedance, and 0.1Hz real impedance between two or more working electrodes may be used forthe detection of sensitivity loss due to biofouling.

In accordance with embodiments of the inventions described herein,EIS-based sensor diagnostics entails consideration and analysis of EISdata relating to one or more of at least three primary factors, i.e.,potential sensor failure modes: (1) signal start-up; (2) signal dip; and(3) sensitivity loss. Significantly, the discovery that a majority ofthe impedance-related parameters that are used in such diagnosticanalyses and procedures can be studied at a frequency, or within a rangeof frequencies, where the parameter is substantially analyte-independentallows for implementation of sensor-diagnostic procedures independentlyof the level of the analyte in a patient's body. Thus, while EIS-basedsensor diagnostics may be triggered by, e.g., large fluctuations inIsig, which is analyte-dependent, the impedance-related parameters thatare used in such sensor diagnostic procedures are themselvessubstantially independent of the level of the analyte. As will beexplored in more detail below, it has also been found that, in amajority of situations where glucose may be seen to have an effect onthe magnitude (or other characteristic) of an EIS-based parameter, sucheffect is usually small enough—e.g., at least an order of magnitudedifference between the EIS-based measurement and the glucose effectthereon—such that it can be filtered out of the measurement, e.g., viasoftware in the IC.

By definition, “start-up” refers to the integrity of the sensor signalduring the first few hours (e.g., t=0-6 hours) after insertion. Forexample, in many current devices, the signal during the first 2 hoursafter insertion is deemed to be unreliable and, as such, the sensorglucose values are blinded to the patient/user. In situations where thesensor takes an extended amount of time to hydrate, the sensor signal islow for several hours after insertion. With the use of EIS, additionalimpedance information is available (by running an EIS procedure) rightafter the sensor has been inserted. In this regard, the total impedanceequation may be used to explain the principle behind low-startupdetection using 1 kHz real impedance. At relatively higherfrequencies—in this case, 1 kHz and above—imaginary impedance is verysmall (as confirmed with in-vivo data), such that total impedancereduces to:

${Z_{t}(\omega)} = {R_{s} + \frac{R_{p}}{1 + {\omega^{2}R_{p}^{2}C_{d}^{2}}}}$

As sensor wetting is gradually completed, the double layer capacitance(C_(d)) increases. As a result, the total impedance will decreasebecause, as indicated in the equation above, total impedance isinversely proportional to C_(d). This is illustrated in the form of theintercept 1600 on the real impedance axis shown, e.g., in FIG. 16B.Importantly, the 1 kHz imaginary impedance can also be used for the samepurpose, as it also includes, and is inversely proportional to, acapacitance component.

Another marker for low startup detection is Nyquist slope, which reliessolely on the relatively lower-frequency impedance which, in turn,corresponds to the Warburg impedance component of total impedance (see,e.g., FIG. 15B). FIG. 22 shows a Nyquist plot for a normally-functioningsensor, where Arrow A is indicative of the progression of time, i.e.,sensor wear time, starting from t=₀. Thus, EIS at the relatively-lowerfrequencies is performed right after sensor insertion (time t=0), whichgenerates real and imaginary impedance data that is plotted with a firstlinear fit 2200 having a first (Nyquist) slope. At a time interval aftert=0, a second (lower) frequency sweep is run that produces a secondlinear fit 2210 having a second (Nyquist) slope larger than the firstNyquist slope, and so on. As the sensor becomes more hydrated, theNyquist slope increases, and the intercept decreases, as reflected bythe lines 2200, 2210, etc. becoming steeper and moving closer to theY-axis. In connection with low startup detection, clinical dataindicates that there is typically a dramatic increase of Nyquist slopeafter sensor insertion and initialization, which is then stabilized to acertain level. One explanation for this is that, as the sensor isgradually wetted, the species diffusivity as well as concentrationundergo dramatic change, which is reflected in Warburg impedance.

In FIG. 23A, the Isig 2230 for a first working electrode WE1 starts offlower than expected (at about 10 nA), and takes some time to catch upwith the Isig 2240 for a second working electrode WE2. Thus, in thisparticular example, WE1 is designated as having a low start-up. The EISdata reflects this low start-up in two ways. First, as shown in FIG.23A, the real impedance at 1 kHz (2235) of WE1 is much higher than the 1kHz real impedance 2245 of WE2. Second, when compared to the Nyquistslope for WE2 (FIG. 23C), the Nyquist slope for WE1 (FIG. 23B) startsout lower, has a larger intercept 2237, and takes more time tostabilize. As will be discussed later, these two signatures—the 1 kHzreal impedance and the Nyquist slope—can be used as diagnostic inputs ina fusion algorithm to decide which of the two electrodes can carry ahigher weight when the fused signal is calculated. In addition, one orboth of these markers may be used in a diagnostic procedure to determinewhether the sensor, as a whole, is acceptable, or whether it should beterminated and replaced.

By definition, signal (or Isig) dips refer to instances of low sensorsignal, which are mostly temporary in nature, e.g., on the order of afew hours. Such low signals may be caused, for example, by some form ofbiological occlusion on the sensor surface, or by pressure applied atthe insertion site (e.g., while sleeping on the side). During thisperiod, the sensor data is deemed to be unreliable; however, the signaldoes recover eventually. In the EIS data, this type of signal dip—asopposed to one that is caused by a glycemic change in the patient'sbody—is reflected in the 1 kHz real impedance data, as shown in FIG. 24.

Specifically, in FIG. 24, both the Isig 2250 for the first workingelectrode WE1 and the Isig 2260 for the second working electrode WE2start out at about 25 nA at the far left end (i.e., at 6 pm). As timeprogresses, both Isigs fluctuate, which is reflective of glucosefluctuations in the vicinity of the sensor. For about the first 12 hoursor so (i.e., until about 6 am), both Isigs are fairly stable, as aretheir respective 1 kHz real impedances 2255, 2265. However, betweenabout 12 and 18 hours—i.e., between 6 am and noon—the Isig 2260 for WE2starts to dip, and continues a downward trend for the next severalhours, until about 9 pm. During this period, the Isig 2250 for WE1 alsoexhibits some dipping, but Isig 2250 is much more stable, and dips quitea bit less, than Isig 2260 for WE2. The behavior of the Isigs for WE1and WE2 is also reflected in their respective 1 kHz real impedance data.Thus, as shown in FIG. 24, during the time period noted above, while the1 kHz real impedance for WE1 (2255) remains fairly stable, there is amarked increase in the 1 kHz real impedance for WE2 (2265).

By definition, sensitivity loss refers to instances where the sensorsignal (Isig) becomes low and non-responsive for an extended period oftime, and is usually unrecoverable. Sensitivity loss may occur for avariety of reasons. For example, electrode poisoning drastically reducesthe active surface area of the working electrode, thereby severelylimiting current amplitude. Sensitivity loss may also occur due tohypoxia, or oxygen deficit, at the insertion site. In addition,sensitivity loss may occur due to certain forms of extreme surfaceocclusion (i.e., a more permanent form of the signal dip caused bybiological or other factors) that limit the passage of both glucose andoxygen through the sensor membrane, thereby lowering thenumber/frequency of the chemical reactions that generate current in theelectrode and, ultimately, the sensor signal (Isig). It is noted thatthe various causes of sensitivity loss mentioned above apply to bothshort-term (7-10 day wear) and long term (6 month wear) sensors.

In the EIS data, sensitivity loss is often preceded by an increase inthe absolute value of phase (|phase|) and of the imaginary impedance(|imaginary impedance|) at the relatively higher frequency ranges (e.g.,128 Hz and above, and 1 kHz and above, respectively). FIG. 25A shows anexample of a normally-functioning glucose sensor where the sensorcurrent 2500 is responsive to glucose—i.e., Isig 2500 tracks glucosefluctuations—but all relevant impedance outputs, such as, e.g., 1 kHzreal impedance 2510, 1 kHz imaginary impedance 2530, and phase forfrequencies at or above about 128 Hz (2520), remain steady, as they aresubstantially glucose-independent.

Specifically, the top graph in FIG. 25A shows that, after the first fewhours, the 1 kHz real impedance 2510 holds fairly steady at about 5kOhms (and the 1 kHz imaginary impedance 2530 holds fairly steady atabout −400 Ohms). In other words, at 1 kHz, the real impedance data 2510and the imaginary impedance data 2530 are substantiallyglucose-independent, such that they can be used as signatures for, orindependent indicators of, the health, condition, and ultimately,reliability of the specific sensor under analysis. However, as mentionedpreviously, different impedance-related parameters may exhibitglucose-independence at different frequency ranges, and the range, ineach case, may depend on the overall sensor design, e.g., electrodetype, surface area of electrode, thickness of membrane, permeability ofmembrane, etc.

Thus, in the example FIG. 25B—for a 90% short tubeless electrodedesign—the top graph again shows that sensor current 2501 is responsiveto glucose, and that, after the first few hours, the 1 kHz realimpedance 2511 holds fairly steady at about 7.5 kOhms. The bottom graphin FIG. 25B shows real impedance data for frequencies between 0.1 Hz(2518) and 1 kHz (2511). As can be seen, the real impedance data at 0.1Hz (2518) is quite glucose-dependent. However, as indicated by referencenumerals 2516, 2514, and 2512, real impedance becomes more and moreglucose-independent as the frequency increases from 0.1 Hz to 1 kHz,i.e., for impedance data measured at frequencies closer to 1 kHz.

Returning to FIG. 25A, the middle graph shows that the phase 2520 at therelatively-higher frequencies is substantially glucose-independent. Itis noted, however, that “relatively-higher frequencies” in connectionwith this parameter (phase) for the sensor under analysis meansfrequencies of 128 Hz and above. In this regard, the graph shows thatthe phase for all frequencies between 128 Hz and 8 kHz is stablethroughout the period shown. On the other hand, as can be seen in thebottom graph of FIG. 25C, while the phase 2522 at 128 Hz (and above) isstable, the phase 2524 fluctuates—i.e., it becomes more and moreglucose-dependent, and to varying degrees—at frequencies that areincreasingly smaller than 128 Hz. It is noted that the electrode designfor the example of FIG. 25C is the same as that used in FIG. 25B, andthat the top graph in the former is identical to the top graph in thelatter.

FIG. 26 shows an example of sensitivity loss due to oxygen deficiency atthe insertion site. In this case, the insertion site becomes oxygendeprived just after day 4 (designated by dark vertical line in FIG. 26),causing the sensor current 2600 to become low and non-responsive. The 1kHz real impedance 2610 remains stable, indicating no physical occlusionon the sensor. However, as shown by the respective downward arrows,changes in the relatively higher-frequency phase 2622 and 1 kHzimaginary impedance 2632 coincide with loss in sensitivity, indicatingthat this type of loss is due to an oxygen deficit at the insertionsite. Specifically, FIG. 26 shows that the phase at higher frequencies(2620) and the 1 kHz imaginary impedance (2630) become more negativeprior to the sensor losing sensitivity-indicated by the dark verticalline—and continue their downward trend as the sensor sensitivity losscontinues. Thus, as noted above, this sensitivity loss is preceded, orpredicted, by an increase in the absolute value of phase (|phase|) andof the imaginary impedance (|imaginary impedance|) at the relativelyhigher frequency ranges (e.g., 128 Hz and above, and 1 kHz and above,respectively).

The above-described signatures may be verified by in-vitro testing, anexample of which is shown in FIG. 27. FIG. 27 shows the results ofin-vitro testing of a sensor, where oxygen deficit at different glucoseconcentrations is simulated. In the top graph, the Isig fluctuates withthe glucose concentration as the latter is increased from 100 mg/dl(2710) to 200 mg/dl (2720), 300 mg/dl (2730), and 400 mg/dl (2740), andthen decreased back down to 200 md/dl (2750). In the bottom graph, thephase at the relatively-higher frequencies is generally stable,indicating that it is glucose-independent. However, at very low oxygenconcentrations, such as, e.g., at 0.1% O₂, the relatively high-frequencyphase fluctuates, as indicated by the encircled areas and arrows 2760,2770. It is noted that the magnitude and/or direction (i.e., positive ornegative) of fluctuation depend on various factors. For example, thehigher the ratio of glucose concentration to oxygen concentration, thehigher the magnitude of the fluctuation in phase. In addition, thespecific sensor design, as well as the age of the sensor (i.e., asmeasured by time after implant), affect such fluctuations. Thus, e.g.,the older a sensor is, the more susceptible it is to perturbations.

FIGS. 28A-28D show another example of oxygen deficiency-led sensitivityloss with redundant working electrodes WE1 and WE2. As shown in FIG.28A, the 1 kHz real impedance 2810 is steady, even as sensor current2800 fluctuates and eventually becomes non-responsive. Also, as before,the change in 1 kHz imaginary impedance 2820 coincides with the sensor'sloss of sensitivity. In addition, however, FIG. 28B shows real impedancedata and imaginary impedance data (2830 and 2840, respectively) at 0.105Hz. The latter, which may be more commonly referred to as “0.1 Hz data”,indicates that, whereas imaginary impedance at 0.1 Hz appears to befairly steady, 0.1 Hz real impedance 2830 increases considerably as thesensor loses sensitivity. Moreover, as shown in FIG. 28C, with loss ofsensitivity due to oxygen deficiency, V_(cntr) 2850 rails to 1.2 Volts.

In short, the diagrams illustrate the discovery that oxygendeficiency-led sensitivity loss is coupled with lower 1 kHz imaginaryimpedance (i.e., the latter becomes more negative), higher 0.105 Hz realimpedance (i.e., the latter becomes more positive), and V_(cntr) rail.Moreover, the oxygen-deficiency process and V_(cntr)-rail are oftencoupled with the increase of the capacitive component in theelectrochemical circuit. It is noted that, in some of the diagnosticprocedures to be described later, the 0.105 Hz real impedance may not beused, as it appears that this relatively lower-frequency real impedancedata may be analyte-dependent.

Finally, in connection with the example of FIGS. 28A-28D, it is notedthat 1 kHz or higher-frequency impedance measurement typically causesEIS-induced spikes in the Isig. This is shown in FIG. 28D, where the rawIsig for WE2 is plotted against time. The drastic increase of Isig whenthe spike starts is a non-Faradaic process, due to double-layercapacitance charge. Thus, oxygen deficiency-led sensitivity loss mayalso be coupled with higher EIS-induced spikes, in addition to lower 1kHz imaginary impedance, higher 0.105 Hz real impedance, and V_(cntr)rail, as discussed above.

FIG. 29 illustrates another example of sensitivity loss. This case maybe thought of as an extreme version of the Isig dip described above inconnection with FIG. 24. Here, the sensor current 2910 is observed to below from the time of insertion, indicating that there was an issue withan insertion procedure resulting in electrode occlusion. The 1 kHzreal-impedance 2920 is significantly higher, while the relativelyhigher-frequency phase 2930 and the 1 kHz imaginary impedance 2940 areboth shifted to much more negative values, as compared to the sameparameter values for the normally-functioning sensor shown in FIG. 25A.The shift in the relatively higher-frequency phase 2930 and 1 kHzimaginary impedance 2940 indicates that the sensitivity loss may be dueto an oxygen deficit which, in turn, may have been caused by anocclusion on the sensor surface.

FIGS. 30A-30D show data for another redundant sensor, where the relativedifferences in 1 kHz real impedance and 1 kHz imaginary impedance, aswell as 0.1 Hz real impedance, between two or more working electrodesmay be used for the detection of sensitivity loss due to biofouling. Inthis example, WE1 exhibits more sensitivity loss than WE2, as is evidentfrom the higher 1 kHz real impedance 3010, lower 1 kHz imaginaryimpedance 3020, and much higher real impedance at 0.105 Hz (3030) forWE2. In addition, however, in this example, V_(cntr) 3050 does not rail.Moreover, as shown in FIG. 30D, the height of the spikes in the raw Isigdata does not change much as time progresses. This indicates that, forsensitivity loss due to biofouling, V_(cntr)-rail and the increase inspike height are correlated. In addition, the fact that the height ofthe spikes in the raw Isig data does not change much with time indicatesthat the capacitive component of the circuit does not changesignificantly with time, such that sensitivity loss due to biofouling isrelated to the resistance component of the circuit (i.e., diffusion).

Various of the above-described impedance-related parameters may be used,either individually or in combination, as inputs into: (1) EIS-basedsensor diagnostic procedures; and/or (2) fusion algorithms forgenerating more reliable sensor glucose values. With regard to theformer, FIG. 31 illustrates how EIS-based data—i.e., impedance-relatedparameters, or characteristics—may be used in a diagnostic procedure todetermine, in real time, whether a sensor is behaving normally, orwhether it should be replaced.

The diagnostic procedure illustrated in the flow diagram of FIG. 31 isbased on the collection of EIS data on a periodic basis, such as, e.g.,hourly, every half hour, every 10 minutes, or at any otherinterval—including continuously—as may be appropriate for the specificsensor under analysis. At each such interval, EIS may be run for anentire frequency spectrum (i.e., a “full sweep”), or it may be run for aselected frequency range, or even at a single frequency. Thus, forexample, for an hourly data collection scheme, EIS may be performed atfrequencies in the μHz to MHz range, or it may be run for a narrowerrange of frequencies, such as, e.g., between about 0.1 Hz and about 8kHz, as discussed hereinabove. In various embodiments, EIS dataacquisition may be implemented alternatingly between a full sweep and annarrower-range spectrum, or in accordance with other schemes.

The temporal frequency of EIS implementation and data collection may bedictated by various factors. For example, each implementation of EISconsumes a certain amount of power, which is typically provided by thesensor's battery, i.e., the battery running the sensor electronics,including the ASIC which is described later. As such, battery capacity,as well as the remaining sensor life, may help determine the number oftimes EIS is run, as well as the breadth of frequencies sampled for eachsuch run. In addition, specific situations may require that an EISparameter at a specific frequency (e.g., real impedance at 1 kHz) bemonitored based on a first schedule (e.g., once every few seconds, orminutes), while other parameters, and/or the same parameter at otherfrequencies, can be monitored based on a second schedule (e.g., lessfrequently). In these situations, the diagnostic procedure can betailored to the specific sensor and requirements, such that batterypower may be preserved, and unnecessary and/or redundant EIS dataacquisition may be avoided.

It is noted that, in certain embodiments, a diagnostic procedure, suchas the one shown in FIG. 31, entails a series of separate “tests” whichare implemented in order to perform real-time monitoring of the sensor.The multiple tests, or markers—also referred to as “multi markers”—areimplemented because each time EIS is run (i.e., each time an EISprocedure is performed), data may be gathered about a multiplicity ofimpedance-based parameters, or characteristics, which can be used todetect sensor condition or quality, including, e.g., whether the sensorhas failed or is failing. In performing sensor diagnostics, sometimes,there can be a diagnostic test that may indicate a failure, whereasother diagnostic(s) may indicate no failure. Therefore, the availabilityof multiple impedance-related parameters, and the implementation of amulti-test procedure, are advantageous, as some of the multiplicity oftests may act as validity checks against some of the other tests. Thus,real-time monitoring using a multi-marker procedure may include acertain degree of built-in redundancy.

With the above in mind, the logic of the diagnostic procedure shown inFIG. 31 begins at 3100, after the sensor has been inserted/implanted,and an EIS run has been made, so as to provide the EIS data as input. At3100, using the EIS data as input, it is first determined whether thesensor is still in place. Thus, if the |Z| slope is found to be constantacross the tested frequency band (or range), and/or the phase angle isabout −90°, it is determined that the sensor is no longer in place, andan alert is sent, e.g., to the patient/user, indicating that sensorpullout has occurred. The specific parameters (and their respectivevalues) described herein for detecting sensor pullout are based on thediscovery that, once the sensor is out of the body and the membrane isno longer hydrated, the impedance spectrum response appears just like acapacitor.

If it is determined that the sensor is still in place, the logic movesto step 3110 to determine whether the sensor is properly initialized. Asshown, the “Init. Check” is performed by determining: (i) whether|(Z_(n)−Z₁)/Z₁|>30% at 1 kHz, where Z₁ is the real impedance measured ata first time, and Z_(n) is the measured impedance at the next interval,at discussed above; and (2) whether the phase angle change is greaterthan 10° at 0.1 Hz. If the answer to either one of the questions is“yes”, then the test is satisfactory, i.e., the Test 1 is not failed.Otherwise, the Test 1 is marked as a failure.

At step 3120, Test 2 asks whether, at a phase angle of −45°, thedifference in frequency between two consecutive EIS runs (f₂−f₁) isgreater than 10 Hz. Again, a “No” answer is marked as a fail; otherwise,Test 2 is satisfactorily met.

Test 3 at step 3130 is a hydration test. Here, the inquiry is whetherthe current impedance Z_(n) is less than the post-initializationimpedance Z_(pi) at 1 kHz. If it is, then this test is satisfied;otherwise, Test 3 is marked as a fail. Test 4 at step 3140 is also ahydration test, but this time at a lower frequency. Thus, this test askswhether Z_(n) is less than 300 kOhms at 0.1 Hz duringpost-initialization sensor operation. Again, a “No” answer indicatesthat the sensor has failed Test 4.

At step 3150, Test 5 inquires whether the low-frequency Nyquist slope isglobally increasing from 0.1 Hz to 1 Hz. As discussed previously, for anormally-operating sensor, the relatively lower-frequency Nyquist slopeshould be increasing over time. Thus, this test is satisfied if theanswer to the inquiry is “yes”; otherwise, the test is marked as failed.

Step 3160 is the last test for this embodiment of the diagnosticprocedure. Here, the inquiry is whether real impedance is globallydecreasing. Again, as was discussed previously, in a normally-operatingsensor, it is expected that, as time goes by, the real impedance shouldbe decreasing. Therefore, a “Yes” answer here would mean that the sensoris operating normally; otherwise, the sensor fails Test 6.

Once all 6 tests have been implemented, a decision is made at 3170 as towhether the sensor is operating normally, or whether it has failed. Inthis embodiment, a sensor is determined to be functioning normally(3172) if it passes at least 3 out of the 6 tests. Put another way, inorder to be determined to have failed (3174), the sensor must fail atleast 4 out of the 6 tests. In alternative embodiments, a different rulemay be used to assess normal operation versus sensor failure. Inaddition, in some embodiments, each of the tests may be weighted, suchthat the assigned weight reflects, e.g., the importance of that test, orof the specific parameter(s) queried for that test, in determiningoverall sensor operation (normal vs. failed). For example, one test maybe weighted twice as heavily as another, but only half as heavily as athird test, etc.

In other alternative embodiments, a different number of tests and/or adifferent set of EIS-based parameters for each test may be used. FIGS.32A and 32B show an example of a diagnostic procedure for real-timemonitoring that includes 7 tests. Referring to FIG. 32A, the logicbegins at 3200, after the sensor has been inserted/implanted, and an EISprocedure has been performed, so as to provide the EIS data as input. At3200, using the EIS data as input, it is first determined whether thesensor is still in place. Thus, if the |Z| slope is found to be constantacross the tested frequency band (or range), and/or the phase angle isabout −90°, it is determined that the sensor is no longer in place, andan alert is sent, e.g., to the patient/user, indicating that sensorpullout has occurred. If, on the other hand, the sensor is determined tobe in place, the logic moves to initiation of diagnostic checks (3202).

At 3205, Test 1 is similar to Test 1 of the diagnostic procedurediscussed above in connection with FIG. 31, except that the instant Test1 specifies that the later measurement Z_(n) is taken 2 hours after thefirst measurement. As such, in this example, Z_(n)=Z_(2hr). Morespecifically, Test 1 compares the real impedance 2 hours after (sensorimplantation and) initialization to the pre-initialization value.Similarly, the second part of Test 1 asks whether the difference betweenthe phase 2 hours after initialization and the pre-initialization phaseis greater than 10° at 0.1 Hz. As before, if the answer to either one ofthe inquiries is affirmative, then it is determined that the sensor ishydrated normally and initialized, and Test 1 is satisfied; otherwise,the sensor fails this test. It should be noted that, even though theinstant test inquires about impedance and phase change 2 hours afterinitialization, the time interval between any two consecutive EIS runsmay be shorter or longer, depending on a variety of factors, including,e.g., sensor design, the level of electrode redundancy, the degree towhich the diagnostic procedure includes redundant tests, battery power,etc.

Moving to 3210, the logic next performs a sensitivity-loss check byinquiring whether, after a 2-hour interval (n+2), the percentage changein impedance magnitude at 1 kHz, as well as that in the Isig, is greaterthan 30%. If the answer to both inquiries is “yes”, then it isdetermined that the sensor is losing sensitivity and, as such, Test 2 isdetermined to be failed. It is noted that, although Test 2 isillustrated herein based on a preferred percentage difference of 30%, inother embodiments, the percentage differences in the impedance magnitudeat 1 kHz and in the Isig may fall within the range 10%-50% for purposesof conducting this test.

Test 3 (at 3220) is similar to Test 5 of the algorithm illustrated inFIG. 31. Here, as before, the question is whether the low-frequencyNyquist slope is globally increasing from 0.1 Hz to 1 Hz. If it is, thenthis test is passed; otherwise, the test is failed. As shown in 3220,this test is also amenable to setting a threshold, or an acceptablerange, for the percent change in the low-frequency Nyquist slope, beyondwhich the sensor may be deemed to be failed or, at the very least, maytrigger further diagnostic testing. In embodiments of the invention,such threshold value/acceptable range for the percent change inlow-frequency Nyquist slope may fall within a range of about 2% to about20%. In some preferred embodiments, the threshold value may be about 5%.

The logic next moves to 3230, which is another low-frequency test, thistime involving the phase and the impedance magnitude. More specifically,the phase test inquires whether the phase at 0.1 Hz is continuouslyincreasing over time. If it is, then the test is failed. As with othertests where the parameter's trending is monitored, the low-frequencyphase test of Test 4 is also amenable to setting a threshold, or anacceptable range, for the percent change in the low-frequency phase,beyond which the sensor may be deemed to be failed or, at the veryleast, raise a concern. In some preferred embodiments, such thresholdvalue/acceptable range for the percent change in low-frequency phase mayfall within a range of about 5% to about 30%. In some preferredembodiments, the threshold value may be about 10%.

As noted, Test 4 also includes a low-frequency impedance magnitude test,where the inquiry is whether the impedance magnitude at 0.1 Hz iscontinuously increasing over time. If it is, then the test is failed. Itis noted that Test 4 is considered “failed” if either the phase test orthe impedance magnitude test is failed. The low-frequency impedancemagnitude test of Test 4 is also amenable to setting a threshold, or anacceptable range, for the percent change in the low-frequency impedancemagnitude, beyond which the sensor may be deemed to be failed or, at thevery least, raise a concern. In some preferred embodiments, suchthreshold value/acceptable range for the percent change in low-frequencyimpedance magnitude may fall within a range of about 5% to about 30%. Insome preferred embodiments, the threshold value may be about 10%, wherethe range for impedance magnitude in normal sensors is generally betweenabout 100 KOhms and about 200 KOhms.

Test 5 (at 3240) is another sensitivity loss check that may be thoughtof as supplemental to Test 2. Here, if both the percentage change in theIsig and the percentage change in the impedance magnitude at 1 kHz aregreater than 30%, then it is determined that the sensor is recoveringfrom sensitivity loss. In other words, it is determined that the sensorhad previously undergone some sensitivity loss, even if the sensitivityloss was not, for some reason, detected by Test 2. As with Test 2,although Test 5 is illustrated based on a preferred percentagedifference of 30%, in other embodiments, the percentage differences inthe Isig and the impedance magnitude at 1 kHz may fall within the range10%-50% for purposes of conducting this test.

Moving to 3250, Test 6 provides a sensor functionality test withspecific failure criteria that have been determined based on observeddata and the specific sensor design. Specifically, in one embodiment, asensor may be determined to have failed and, as such, to be unlikely torespond to glucose, if at least two out of the following three criteriaare met: (1) Isig is less than 10 nA; and (2) the imaginary impedance at1 kHz is less than −1500 Ohm; and (3) the phase at 1 kHz is less than−15°. Thus, Test 6 is determined to have been passed if any two of(1)-(3) are not met. It is noted that, in other embodiments, the Isigprong of this test may be failed if the Isig is less than about 5 nA toabout 20 nA. Similarly, the second prong may be failed if the imaginaryimpedance at 1 kHz is less than about −1000 Ohm to about −2000 Ohms.Lastly, the phase prong may be failed if the phase at 1 kHz is less thanabout −10° to about −20°.

Lastly, step 3260 provides another sensitivity check, wherein theparameters are evaluated at low frequency. Thus, Test 7 inquireswhether, at 0.1 Hz, the magnitude of the difference between the ratio ofthe imaginary impedance to the Isig (n+2), on the one hand, and thepervious value of the ratio, on the other, is larger than 30% of themagnitude of the previous value of the ratio. If it is, then the test isfailed; otherwise, the test is passed. Here, although Test 7 isillustrated based on a preferred percentage difference of 30%, in otherembodiments, the percentage difference may fall within the range 10%-50%for purposes of conducting this test.

Once all 7 tests have been implemented, a decision is made at 3270 as towhether the sensor is operating normally, or whether an alert should besent out, indicating that the sensor has failed (or may be failing). Asshown, in this embodiment, a sensor is determined to be functioningnormally (3272) if it passes at least 4 out of the 7 tests. Put anotherway, in order to be determined to have failed, or to at least raise aconcern (3274), the sensor must fail at least 4 out of the 7 tests. Ifit is determined that the sensor is “bad” (3274), an alert to thateffect may be sent, e.g., to the patient/user. As noted previously, inalternative embodiments, a different rule may be used to assess normaloperation versus sensor failure/concern. In addition, in someembodiments, each of the tests may be weighted, such that the assignedweight reflects, e.g., the importance of that test, or of the specificparameter(s) queried for that test, in determining overall sensoroperation (normal vs. failed).

As was noted previously, in embodiments of the inventions describedherein, various of the above-described impedance-related parameters maybe used, either individually or in combination, as inputs into one ormore fusion algorithms for generating more reliable sensor glucosevalues. Specifically, it is known that, unlike a single-sensor (i.e., asingle-working-electrode) system, multiple sensing electrodes providehigher-reliability glucose readouts, as a plurality of signals, obtainedfrom two or more working electrodes, may be fused to provide a singlesensor glucose value. Such signal fusion utilizes quantitative inputsprovided by EIS to calculate the most reliable output sensor glucosevalue from the redundant working electrodes. It is noted that, while theensuing discussion may describe various fusion algorithms in terms of afirst working electrode (WE1) and a second working electrode (WE2) asthe redundant electrodes, this is by way of illustration, and notlimitation, as the algorithms and their underlying principles describedherein are applicable to, and may be used in, redundant sensor systemshaving more than 2 working electrodes. In addition, the redundantelectrodes may be included in (identical) sensors on/within a singleflex or multiple flexes, or the redundant electrodes may be included innon-identical sensors (e.g., in a complex redundant sensor system havingtwo or more sensors, wherein at least two of the sensors have differentdesigns than one another) on/within a single flex or multiple flexes.

FIGS. 33A and 33B show top-level flowcharts for two alternativemethodologies, each of which includes a fusion algorithm. Specifically,FIG. 33A is a flowchart involving a current (Isig)-based fusionalgorithm, and FIG. 33B is a flowchart directed to sensor glucose (SG)fusion. As may be seen from the diagrams, the primary difference betweenthe two methodologies is the time of calibration. Thus, FIG. 33A showsthat, for Isig fusion, calibration 3590 is performed after the fusion3540 is completed. That is, redundant Isigs from WE1 to WEn are fusedinto a single Isig 3589, which is then calibrated to produce a singlesensor glucose value 3598. For SG fusion, on the other hand, calibration3435 is completed for each individual Isig from WE1 to WEn to producecalibrated SG values (e.g., 3436, 3438) for each of the workingelectrodes. Thus, SG fusion algorithms provide for independentcalibration of each of the plurality of Isigs, which may be preferred insome embodiments of the inventions described herein. Once calibrated,the plurality of calibrated SG values is fused into a single SG value3498.

It is important to note that each of flowcharts shown in FIGS. 33A and33B includes a spike filtering process (3520, 3420). As was describedabove in the discussion relating to sensitivity loss, 1 kHz orhigher-frequency impedance measurements typically cause EIS-inducedspikes in the Isig. Therefore, once an EIS procedure has been performedfor each of the electrodes WE1 to WEn, for both SG fusion and Isigfusion, it is preferable to first filter the Isigs 3410, 3412, etc. and3510, 3512, etc. to obtain respective filtered Isigs 3422, 3424, etc.and 3522, 3524, etc. The filtered Isigs are then either used in Isigfusion, or first calibrated and then used in SG fusion, as detailedbelow. As will become apparent in the ensuing discussion, both fusionalgorithms entail calculation and assignment of weights based on variousfactors.

FIG. 34 shows the details of the fusion algorithm 3440 for SG fusion.Essentially, there are four factors that need to be checked before thefusion weights are determined. First, integrity check 3450 involvesdetermining whether each of the following parameters is within specifiedranges for normal sensor operation (e.g., predetermined lower and upperthresholds): (i) Isig; (ii) 1 kHz real and imaginary impedances; (iii)0.105 Hz real and imaginary impedances; and (iv) Nyquist slope. Asshown, integrity check 3450 includes a Bound Check 3452 and a NoiseCheck 3456, wherein, for each of the Checks, the above-mentionedparameters are used as input parameters. It is noted that, for brevity,real and/or imaginary impedances, at one or more frequencies, appear onFIGS. 33A-35 simply as “Imp” for impedance. In addition, both real andimaginary impedances may be calculated using impedance magnitude andphase (which is also shown as an input on FIGS. 33A and 33B).

The output from each of the Bound Check 3452 and the Noise Check 3458 isa respective reliability index (RI) for each of the redundant workingelectrodes. Thus, the output from the Bound Check includes, e.g.,RI_bound_We₁ (3543) and RI_bound_We₂ (3454). Similarly, for the NoiseCheck, the output includes, e.g., RI_noise_We₁ (3457) and RI_noise_We₂(3458). The bound and noise reliability indices for each workingelectrode are calculated based on compliance with the above-mentionedranges for normal sensor operation. Thus, if any of the parameters fallsoutside the specified ranges for a particular electrode, the reliabilityindex for that particular electrode decreases.

It is noted that the threshold values, or ranges, for theabove-mentioned parameters may depend on various factors, including thespecific sensor and/or electrode design. Nevertheless, in one preferredembodiment, typical ranges for some of the above-mentioned parametersmay be, e.g., as follows: Bound threshold for 1 kHz realimpedance=[0.3e+4 2e+4]; Bound threshold for 1 kHz imaginaryimpedance=[−2e+3, 0]; Bound threshold for 0.105 Hz real impedance=[2e+47e+4]; Bound threshold for 0.105 Hz imaginary impedance=[−2e+5−0.25e+5];and Bound threshold for Nyquist slope=[2 5]. Noise may be calculated,e.g., using a second order central difference method where, if noise isabove a certain percentage (e.g., 30%) of median value for each variablebuffer, it is considered to be out of noise bound.

Second, sensor dips may be detected using sensor current (Isig) and 1kHz real impedance. Thus, as shown in FIG. 34, Isig and “Imp” are usedas inputs for dips detection 3460. Here, the first step is to determinewhether there is any divergence between Isigs, and whether any suchdivergence is reflected in 1 kHz real impedance data. This may beaccomplished by using mapping 3465 between the Isig similarity index(RI_sim_isig12) 3463 and the 1 kHz real impedance similarity index(RI_sim_imp12) 3464. This mapping is critical, as it helps avoid falsepositives in instances where a dip is not real. Where the Isigdivergence is real, the algorithm will select the sensor with the higherIsig.

In accordance with one embodiment, the divergence/convergence of twosignals (e.g., two Isigs, or two 1 kHz real impedance data points) canbe calculated as follows:

diff_va1=abs(va1−(va1+va2)/2);

diff_va2=abs(va2−(va1+va2)/2);

RI_sim=1−(diff_va1+diff_va2)/(mean(abs(val+va2))/4)

where va1 and va2 are two variables, and RI_sim (similarity index) isthe index to measure the convergence or divergence of the signals. Inthis embodiment, RI_sim must be bound between 0 and 1. Therefore, ifRI_sim as calculated above is less than 0, it will be set to 0, and ifit is higher than 1, it will be set to 1.

The mapping 3465 is performed by using ordinary linear regression (OLR).However, when OLR does not work well, a robust median slope linearregression (RMSLR) can be used. For Isig similarity index and 1 kHz realimpedance index, for example, two mapping procedures are needed: (i) MapIsig similarity index to 1 kHz real impedance similarity index; and (ii)map 1 kHz real impedance similarity index to Isig similarity index. Bothmapping procedures will generate two residuals: res12 and res21. Each ofthe dip reliability indices 3467, 3468 can then be calculated as:

RI_dip=1−(res12+res21)/(RI_sim_isig+RI_sim_1K_real_impedance).

The third factor is sensitivity loss 3470, which may be detected using 1kHz imaginary impedance trending in, e.g., the past 8 hours. If onesensor's trending turns negative, the algorithm will rely on the othersensor. If both sensors lose sensitivity, then a simple average istaken. Trending may be calculated by using a strong low-pass filter tosmooth over the 1 kHz imaginary impedance, which tends to be noisy, andby using a correlation coefficient or linear regression with respect totime during, e.g., the past 8 hours to determine whether the correlationcoefficient is negative or the slope is negative. Each of thesensitivity loss reliability indices 3473, 3474 is then assigned abinary value of 1 or 0.

The total reliability index (RI) for each of we1, we2, . . . wen iscalculated as follows:

RI_we₁ = RI_dip_we₁ × RI_sensitivity_loss_we₁ × RI_bound_we₁ × RI_noise_we₁RI_we₂ = RI_dip_we₂ × RI_sensitivity_loss_we₂ × RI_bound_we₂ × RI_noise_we₂RI_we₃ = RI_dip_we₃ × RI_sensitivity_loss_we₃ × RI_bound_we₃ × RI_noise_we₃RI_we₄ = RI_dip_we₄ × RI_sensitivity_loss_we₄ × RI_bound_we₄ × RI_noise_we₄⋮RI_we_(n) = RI_dip_we_(n) × RI_sensitivity_loss_we_(n) × RI_bound_we_(n) × RI_noise_we_(n)

Having calculated the respective reliability indices of the individualworking electrodes, the weight for each of the electrodes may becalculated as follow:

weight_we₁ = RI_we₁/(RI_we₁ + RI_we₂ + RI_we₃ + RI_we₄ + … + RI_we_(n))weight_we₂ = RI_we₂/(RI_we₁ + RI_we₂ + RI_we₃ + RI_we₄ + … + RI_we_(n))weight_we₃ = RI_we₃/(RI_we₁ + RI_we₂ + RI_we₃ + RI_we₄ + … + RI_we_(n))weight_we₄ = RI_we₄/(RI_we₁ + RI_we₂ + RI_we₃ + RI_we₄ + … + RI_we_(n))⋮weight_we_(n) = RI_we_(n)/(RI_we₁ + RI_we₂ + RI_we₃ + RI_we₄ + … + RI_we_(n))

Based on the above, the fused SG 3498 is then calculated as follows:

SG=weight_we ₁ ×SG_we ₁+weight_we ₂ ×SG_we ₂+weight_we ₃ ×SG_we₃+weight_we ₄ ×SG_we ₄+ . . . +weight_we _(n) ×SG_we _(n)

The last factor relates to artifacts in the final sensor readout, suchas may be caused by instant weight change of sensor fusion. This may beavoided by either applying a low-pass filter 3480 to smooth the RI foreach electrode, or by applying a low-pass filter to the final SG. Whenthe former is used, the filtered reliability indices—e.g., RI_We1* andRI_We2* (3482, 3484)—are used in the calculation of the weight for eachelectrode and, therefore, in the calculation of the fused SG 3498.

FIG. 35 shows the details of the fusion algorithm 3540 for Isig fusion.As can be seen, this algorithm is substantially similar to the one shownin FIG. 34 for SG fusion, with two exceptions. First, as was notedpreviously, for Isig fusion, calibration constitutes the final step ofthe process, where the single fused Isig 3589 is calibrated to generatea single sensor glucose value 3598. See also FIG. 33B. Second, whereasSG fusion uses the SG values for the plurality of electrodes tocalculate the final SG value 3498, the fused Isig value 3589 iscalculated using the filtered Isigs (3522, 3524, and so on) for theplurality of electrodes.

In one closed-loop study involving a non-diabetic population, it wasfound that the above-described fusion algorithms provided considerableimprovements in the Mean Absolute Relative Difference (MARD) both on Day1, when low start-up issues are most significant and, as such, may havea substantial impact on sensor accuracy and reliability, and overall(i.e., over a 7-day life of the sensor). The study evaluated data for an88% distributed layout design with high current density (nominal)plating using three different methodologies: (1) calculation of onesensor glucose value (SG) via fusion using Medtronic Minimed's FerrariAlgorithm 1.0 (which is a SG fusion algorithm as discussed above); (2)calculation of one SG by identifying the better ISIG value using 1 kHzEIS data (through the Isig fusion algorithm discussed above); and (3)calculation of one SG by using the higher ISIG value (i.e., withoutusing EIS). The details of the data for the study are presented below:

(1) SG Based on Ferrari 1.0 Alg for 88% Distributed Layout with HighCurrent Density (Nominal) Plating

Mean-ARD Percentage Day 1 2 3 4 5 6 7 Total 040-080 19.39 17.06 22.2717.50 37.57 11.43 19.69 080-120 19.69 09.18 09.34 08.64 10.01 08.3111.33 11.56 120-240 19.01 17.46 12.44 07.97 11.75 08.82 12.15 12.92240-400 10.25 08.36 14.09 10.86 12.84 22.70 12.88 Total 19.52 11.7110.14 09.30 10.83 09.49 11.89 12.28

Mean-Absolute Bias (sg-bg) Day 1 2 3 4 5 6 7 Total 040-080 14.86 11.7815.81 11.07 29.00 07.26 14.05 080-120 19.53 09.37 09.49 08.78 09.8808.44 11.61 11.62 120-240 30.04 29.73 19.34 14.45 18.25 12.66 18.8920.60 240-400 26.75 22.23 39.82 29.00 33.00 61.36 35.19 Total 21.6215.20 12.79 13.21 12.04 10.84 15.04 14.79

Mean−Signed Bias (sg-bg) Day 1 2 3 4 5 6 7 Total 040-080 12.15 09.7815.81 11.07 29.00 07.26 13.01 080-120 −04.45 −04.92 −00.90 00.18 01.2100.85 00.03 −01.44 120-240 −10.18 −27.00 −16.89 −02.91 −05.40 −01.24−11.58 −10.71 240-400 11.25 02.23 −00.07 −27.00 −33.00 −61.36 −10.29Total −04.81 −09.77 −05.09 −00.23 −00.22 00.67 −04.98 −03.56

Eval Points Day 1 2 3 4 5 6 7 Total 040-080 007 004 000 002 006 003 004026 080-120 090 064 055 055 067 056 047 434 120-240 028 025 022 021 016032 026 170 240-400 000 002 004 008 003 001 002 020 Total 125 095 081086 092 092 079 650

(2) SG Based on Better ISIG Using 1 kHz EIS for 88% Distributed Layoutwith High Current Density (Nominal) Plating

Mean-ARD Percentage Day 1 2 3 4 5 6 7 Total 040-080 16.66 18.78 21.1316.21 43.68 09.50 18.14 080-120 16.22 11.96 08.79 10.49 09.75 08.0410.34 11.36 120-240 15.08 17.50 12.68 07.72 08.74 08.84 13.02 12.16240-400 07.66 06.42 11.10 07.52 15.95 21.13 09.84 Total 15.96 13.7009.92 09.95 09.96 09.40 11.31 11.83

Mean-Absolute Bias (sg-bg) Day 1 2 3 4 5 6 7 Total 040-080 12.71 13.0015.00 10.17 33.50 06.00 12.83 080-120 15.70 12.17 08.57 10.89 09.6208.26 10.49 11.32 120-240 24.43 29.82 19.43 13.79 14.60 12.97 20.2719.58 240-400 20.00 17.00 32.50 20.00 41.00 60.00 27.29 Total 17.7217.20 12.56 13.55 10.95 11.21 14.12 14.20

Mean-Signed Bias (sg-bg) Day 1 2 3 4 5 6 7 Total 040-080 08.71 13.0015.00 10.17 33.50 06.00 11.67 080-120 −04.30 −08.62 −01.11 −03.64 02.5200.40 −01.56 −02.52 120-240 −11.30 −29.64 −17.09 −08.74 −10.87 −07.23−15.09 −14.05 240-400 20.00 00.50 09.50 −17.33 −41.00 −60.00 −03.18Total −05.30 −12.56 −06.20 −03.63 −00.10 −02.29 −06.35 −05.21

Eval Points Day 1 2 3 4 5 6 7 Total 040-080 007 004 000 001 006 002 004024 080-120 082 053 044 045 058 043 041 366 120-240 030 022 023 019 015030 022 161 240-400 000 002 004 006 003 001 001 017 Total 119 081 071071 082 076 068 568

(3) SG Based on Higher ISIG for 88% Distributed Layout with High CurrentDensity (Nominal) Plating

Mean-ARD Percentage Day 1 2 3 4 5 6 7 Total 040-080 17.24 19.13 21.1317.31 43.68 10.38 18.79 080-120 17.69 11.77 09.36 10.70 10.19 08.3410.68 11.86 120-240 16.80 17.63 13.04 07.38 09.04 08.52 13.25 12.50240-400 07.47 06.02 10.85 07.52 15.95 21.13 09.63 Total 17.44 13.6010.37 10.00 10.40 09.36 11.66 12.26

Mean-Absolute Bias (sg-bg) Day 1 2 3 4 5 6 7 Total 040-080 13.14 13.2515.00 11.00 33.50 06.50 13.29 080-120 17.23 11.98 09.22 11.02 10.0808.59 10.86 11.85 120-240 27.40 30.09 19.75 13.26 14.93 12.45 20.6520.09 240-400 19.50 16.00 32.00 20.00 41.00 60.00 26.82 Total 19.5317.09 13.00 13.35 11.37 11.18 14.53 14.67

Mean-Signed Bias (sg-bg) Day 1 2 3 4 5 6 7 Total 040-080 08.29 12.7515.00 11.00 33.50 06.50 11.79 080-120 −04.72 −08.83 −02.35 −01.56 01.75−00.18 −01.52 −02.70 120-240 −15.13 −29.73 −17.67 −08.42 −11.47 −07.03−15.43 −14.86 240-400 19.50 01.50 06.33 −17.33 −41.00 −60.00 −04.12Total −06.57 −12.70 −07.11 −02.46 −00.63 −02.56 −06.47 −05.57

Eval Points Day 1 2 3 4 5 6 7 Total 040-080 007 004 000 001 006 002 004024 080-120 083 054 046 048 060 044 042 377 120-240 030 022 024 019 015031 023 164 240-400 000 002 004 006 003 001 001 017 Total 120 082 074074 084 078 070 582

With the above data, it was found that, with the first approach, theMARD (%) on Day 1 was 19.52%, with an overall MARD of 12.28%. For thesecond approach, the Day-1 MARD was 15.96% and the overall MARD was11.83%. Lastly, for the third approach, the MARD was 17.44% on Day 1,and 12.26% overall. Thus, for this design with redundant electrodes, itappears that calculation of SG based on the better ISIG using 1 kHz EIS(i.e., the second methodology) provides the greatest advantage.Specifically, the lower Day-1 MARD may be attributable, e.g., to betterlow start-up detection using EIS. In addition, the overall MARDpercentages are more than 1% lower than the overall average MARD of13.5% for WE1 and WE2 in this study. It is noted that, in theabove-mentioned approaches, data transitions may be handled, e.g., by afiltering method to minimize the severity of the transitions, such as byusing a low-pass filter 3480 as discussed above in connection with FIGS.33A-35.

It bears repeating that sensor diagnostics, including, e.g., assessmentof low start-up, sensitivity-loss, and signal-dip events depends onvarious factors, including the sensor design, number of electrodes(i.e., redundancy), electrode distribution/configuration, etc. As such,the actual frequency, or range of frequencies, for which an EIS-basedparameter may be substantially glucose-independent, and therefore, anindependent marker, or predictor, for one or more of the above-mentionedfailure modes may also depend on the specific sensor design. Forexample, while it has been discovered, as described hereinabove, thatsensitivity loss may be predicted using imaginary impedance at therelatively higher frequencies—where imaginary impedance is substantiallyglucose-independent—the level of glucose dependence, and, therefore, thespecific frequency range for using imaginary impedance as a marker forsensitivity loss, may shift (higher or lower) depending on the actualsensor design.

More specifically, as sensor design moves more and more towards the useof redundant working electrodes, the latter must be of increasinglysmaller sizes in order to maintain the overall size of the sensor. Thesize of the electrodes, in turn, affects the frequencies that may bequeried for specific diagnostics. In this regard, it is important tonote that the fusion algorithms described herein and shown in FIGS.33A-35 are to be regarded as illustrative, and not limiting, as eachalgorithm can be modified as necessary to use EIS-based parameters atfrequencies that exhibit the least amount of glucose dependence, basedon the type of sensor under analysis.

In addition, experimental data indicates that human tissue structure mayalso affect glucose dependence at different frequencies. For example, inchildren, real impedance at 0.105 Hz has been found to be asubstantially glucose-independent indicator for low start-up detection.It is believed that this comes about as a result of a child's tissuestructure changing, e.g., the Warburg impedance, which relates mostly tothe resistive component. See also the subsequent discussion relating tointerferent detection.

Embodiments of the inventions described herein are also directed to theuse of EIS in optimizing sensor calibration. By way of background, incurrent methodologies, the slope of a BG vs. Isig plot, which may beused to calibrate subsequent Isig values, is calculated as follows:

${slope} = \frac{\sum{{{\alpha\beta}\left( {{isig} - {offset}} \right)}{bg}}}{\sum{\alpha \; {\beta \left( {{isig} - {offset}} \right)}^{2}}}$

where α is an exponential function of a time constant, β is a functionof blood glucose variance, and offset is a constant. For a sensor insteady condition, this method provides fairly accurate results. Asshown, e.g., in FIG. 36, BG and Isig follow a fairly linearrelationship, and offset can be taken as a constant.

However, there are situations in which the above-mentioned linearrelationship does not hold true, such as, e.g., during periods in whichthe sensor experiences a transition. As shown in FIG. 37, it is clearthat Isig-BG pairs 1 and 2 are significantly different from pairs 3 and4 in terms of Isig and BG relationship. For these types of conditions,use of a constant offset tends to produce inaccurate results.

To address this issue, one embodiment is directed to the use of anEIS-based dynamic offset, where EIS measurements are used to define asensor status vector as follows:

V=(real_imp_1K,img_imp_1K,Nyquist_slope,Nyquist_R_square)

where all of the elements in the vector are substantially BGindependent. It is noted that Nyquist_R_square is the R square of linearregression used to calculate the Nyquist slope, i.e., the square of thecorrelation coefficient between real and imaginary impedances atrelatively-lower frequencies, and a low R square indicates abnormalityin sensor performance. For each Isig-BG pair, a status vector isassigned. If a significant difference in status vector is detected—e.g.,|V2−V3| for the example shown in FIG. 37—a different offset value isassigned for 3 and 4 when compared to 1 and 2. Thus, by using thisdynamic offset approach, it is possible to maintain a linearrelationship between Isig and BG.

In a second embodiment, an EIS-based segmentation approach may be usedfor calibration. Using the example of FIG. 37 and the vector V, it canbe determined that sensor state during 1 and 2 is significantlydifferent from sensor state during 3 and 4. Therefore, the calibrationbuffer can be divided into two segments, as follows:

Isig_buffer1=[sig1,Isig2];BG_buffer1=[BG1,BG2]

Isig_buffer2=[Isig3,Isig4];BG_buffer2=[BG3,BG4]

Thus, when the sensor operates during 1 and 2, Isig_buffer1 andBG_buffer1 would be used for calibration. However, when the sensoroperates during 3 and 4, i.e., during a transition period, Isig_buffer2and BG_buffer2 would be used for calibration.

In yet another embodiment, an EIS-based dynamic slope approach, whereEIS is used to adjust slope, may be used for calibration purposes. FIG.38A shows an example of how this method can be used to improve sensoraccuracy. In this diagram, the data points 1-4 are discrete bloodglucose values. As can be seen from FIG. 38A, there is a sensor dip 3810between data points 1 and 3, which dip can be detected using the sensorstate vector V described above. During the dip, slope can be adjustedupward to reduce the underreading, as shown by reference numeral 3820 inFIG. 38A.

In a further embodiment, EIS diagnostics may be used to determine thetiming of sensor calibrations, which is quite useful for, e.g,low-startup events, sensitivity-loss events, and other similarsituations. As is known, most current methodologies require regularcalibrations based on a pre-set schedule, e.g., 4 times per day. UsingEIS diagnostics, however, calibrations become event-driven, such thatthey may be performed only as often as necessary, and when they would bemost productive. Here, again, the status vector V may be used todetermine when the sensor state has changed, and to request calibrationif it has, indeed, changed.

More specifically, in an illustrative example, FIG. 38B shows aflowchart for EIS-assisted sensor calibration involving low start-updetection. Using Nyquist slope, 1 kHz real impedance, and a bound check3850 (see, e.g., the previously-described bound check and associatedthreshold values for EIS-based parameters in connection with the fusionalgorithms of FIGS. 33A-35), a reliability index 3853 can be developedfor start-up, such that, when the 1 kHz real impedance 3851 and theNyquist slope 3852 are lower than their corresponding upper bounds,RI_startup=1, and sensor is ready for calibration. In other words, thereliability index 3853 is “high” (3854), and the logic can proceed tocalibration at 3860.

When, on the other hand, the 1 kHz real impedance and the Nyquist slopeare higher than their corresponding upper bounds (or threshold values),RI_startup=0 (i.e., it is “low”), and the sensor is not ready forcalibration (3856), i.e., a low start-up issue may exist. Here, thetrend of 1 kHz real impedance and the Nyquist slope can be used topredict when both parameters will be in range (3870). If it is estimatedthat this will only take a very short amount of time (e.g., less thanone hour), then the algorithm waits until the sensor is ready, i.e.,until the above-mentioned EIS-based parameters are in-bound (3874), atwhich point the algorithm proceeds to calibration. If, however, the waittime would be relatively long (3876), then the sensor can be calibratednow, and then the slope or offset can be gradually adjusted according tothe 1 kHz real impedance and the Nyquist slope trend (3880). It is notedthat by performing the adjustment, serious over- or under-reading causedby low start-up can be avoided. As noted previously, the EIS-basedparameters and related information that is used in the instantcalibration algorithm is substantially glucose-independent.

It is noted that, while the above description in connection with FIG.38B shows a single working electrode, as well as the calculation of areliability index for start-up of that working electrode, this is by wayof illustration, and not limitation. Thus, in a redundant sensorincluding two or more working electrodes, a bound check can beperformed, and a start-up reliability index calculated, for each of theplurality of (redundant) working electrodes. Then, based on therespective reliability indices, at least one working electrode can beidentified that can proceed to obtain glucose measurements. In otherwords, in a sensor having a single working electrode, if the latterexhibits low start-up, actual use of the sensor (for measuring glucose)may have to be delayed until the low start-up period is over. Thisperiod may typically be on the order of one hour or more, which isclearly disadvantageous. In contrast, in a redundant sensor, utilizingthe methodology described herein allows an adaptive, or “smart”,start-up, wherein an electrode that can proceed to data gathering can beidentified in fairly short order, e.g., on the order of a few minutes.This, in turn, reduces MARD, because low start-up generally providesabout a ½% increase in MARD.

In yet another embodiment, EIS can aid in the adjustment of thecalibration buffer. For existing calibration algorithms, the buffer sizeis always 4, i.e., 4 Isig-BG pairs, and the weight is based upon αwhich, as noted previously, is an exponential function of a timeconstant, and β, which is a function of blood glucose variance. Here,EIS can help to determine when to flush the buffer, how to adjust bufferweight, and what the appropriate buffer size is.

In some embodiments, EIS may also be used for interferent detection.Specifically, it may be desirable to provide a medication infusion setthat includes a combination sensor and medication-infusion catheter,where the sensor is placed within the infusion catheter. In such asystem, the physical location of the infusion catheter relative to thesensor may be of some concern, due primarily to the potential impact on(i.e., interference with) sensor signal that may be caused by themedication being infused and/or an inactive component thereof.

For example, the diluent used with insulin contains m-cresol as apreservative. In in-vitro studies, m-cresol has been found to negativelyimpact a glucose sensor if insulin (and, therefore, m-cresol) is beinginfused in close proximity to the sensor. Therefore, a system in which asensor and an infusion catheter are to be combined in a single needlemust be able to detect, and adjust for, the effect of m-cresol on thesensor signal. Since m-cresol affects the sensor signal, it would bepreferable to have a means of detecting this interferent independentlyof the sensor signal itself.

Experiments have shown that the effect of m-cresol on the sensor signalis temporary and, thus, reversible. Nevertheless, when insulin infusionoccurs too close to the sensor, the m-cresol tends to “poison” theelectrode(s), such that the latter can no longer detect glucose, untilthe insulin (and m-cresol) have been absorbed into the patient's tissue.In this regard, it has been found that there is typically about a40-minute time period between initiation of insulin infusion and whenthe sensor has re-gained the ability to detect glucose again. However,advantageously, it has also been discovered that, during the same timeperiod, there is a large increase in 1 kHz impedance magnitude quiteindependently of the glucose concentration.

Specifically, FIG. 39 shows Isig and impedance data for an in-vitroexperiment, wherein the sensor was placed in a 100 mg/dL glucosesolution, and 1 kHz impedance was measured every 10 minutes, as shown byencircled data points 3920. m-cresol was then added to bring thesolution to 0.35% m-cresol (3930). As can be seen, once m-cresol hasbeen added, the Isig 3940 initially increases dramatically, and thenbegins to drift down. The concentration of glucose in the solution wasthen doubled, by adding an additional 100 mg/dL glucose. This, however,had no effect on the Isig 3940, as the electrode was unable to detectthe glucose.

On the other hand, the m-cresol had a dramatic effect on both impedancemagnitude and phase. FIG. 40A shows a Bode plot for the phase, and FIG.40B shows a Bode plot for impedance magnitude, for both before and afterthe addition of m-cresol. As can be seen, after the m-cresol was added,the impedance magnitude 4010 increased from its post-initializationvalue 4020 by at least an order of magnitude across the frequencyspectrum. At the same time, the phase 4030 changed completely ascompared to its post-initialization value 4040. On the Nyquist plot ofFIG. 40C. Here, the pre-initialization curve 4050 and thepost-initialization curve 4060 appear as expected for anormally-functioning sensor. However, after the addition of m-cresol,the curve 4070 becomes drastically different.

The above experiment identifies an important practical pitfall ofcontinuing to rely on the Isig after m-cresol has been added. Referringback to FIG. 39, a patient/user monitoring the sensor signal may be putunder the mistaken impression that his glucose level has just spiked,and that he should administer a bolus. The user then administers thebolus, at which the Isig has already started to drift back down. Inother words, to the patient/user, everything may look normal. Inreality, however, what has really happened is that the patient justadministered an unneeded dose of insulin which, depending on thepatient's glucose level prior to administration of the bolus, may putthe patient at risk of experiencing a hypoglycemic event. This scenarioreinforces the desirability of a means of detecting interferents that isas glucose-independent as possible.

FIG. 41 shows another experiment, where a sensor was initialized a 100mg/dL glucose solution, after which glucose was raised to 400 mg/dL forone hour, and then returned to 100 mg/dL. m-cresol was then added toraise the concentration to 0.35%, with the sensor remaining in thissolution for 20 minutes. Finally, the sensor was placed in a 100 mg/dLglucose solution to allow Isig to recover after exposure to m-cresol. Ascan be seen, after initialization, the 1 kHz impedance magnitude 4110was at about 2 kOhms. When m-cresol was added, the Isig 4120 spiked, asdid impedance magnitude 4110. Moreover, when the sensor was returned toa 100 md/dL glucose solution, the impedance magnitude 4110 also returnedto near normal level.

As can be seen from the above experiments, EIS can be used to detect thepresence of an interfering agent—in this case, m-cresol. Specifically,since the interferent affects the sensor in such a way as to increasethe impedance magnitude across the entire frequency spectrum, theimpedance magnitude may be used to detect the interference. Once theinterference has been detected, either the sensor operating voltage canbe changed to a point where the interferent is not measured, or datareporting can be temporarily suspended, with the sensor indicating tothe patient/user that, due to the administration of medication, thesensor is unable to report data (until the measured impedance returns tothe pre-infusion level). It is noted that, since the impact of theinterferent is due to the preservative that is contained in insulin, theimpedance magnitude will exhibit the same behavior as described aboveregardless of whether the insulin being infused is fast-acting or slow.

Importantly, as mentioned above, the impedance magnitude, and certainlythe magnitude at 1 kHz, is substantially glucose-independent. Withreference to FIG. 41, it can be seen that, as the concentration ofglucose is raised from 100 mg/dL to 400 mg/dL—a four-fold increase—the 1kHz impedance magnitude increase from about 2000 Ohms to about 2200Ohms, or about a 10% increase. In other words, the effect of glucose onthe impedance magnitude measurement appears to be about an order ofmagnitude smaller compared to the measured impedance. This level of“signal-to-noise” ratio is typically small enough to allow the noise(i.e., the glucose effect) to be filtered out, such that the resultantimpedance magnitude is substantially glucose-independent. In addition,it should be emphasized that the impedance magnitude exhibits an evenhigher degree of glucose-independence in actual human tissue, ascompared to the buffer solution that was used for the in-vitroexperiments described above.

Embodiments of the inventions described herein are also directed to anAnalog Front End Integrated Circuit (AFE IC), which is a customApplication Specific Integrated Circuit (ASIC) that provides thenecessary analog electronics to provide the following, among others: (i)support multiple potentiostats and interface with multi-terminal glucosesensors based on either Oxygen or Peroxide; (ii) interface with amicrocontroller so as to form a micropower sensor system; and (iii)implement EIS diagnostics, fusion algorithms, and other EIS-basedprocesses based on measurement of EIS-based parameters. Morespecifically, the ASIC incorporates diagnostic capability to measure thereal and imaginary impedance parameters of the sensor(s) over a widerange of frequencies, as well as digital interface circuitry to enablebidirectional communication with a microprocessor chip. Moreover, theASIC includes power control circuitry that enables operation at very lowstandby and operating power, and a real-time clock and a crystaloscillator so that an external microprocessor's power can be turned off.

FIGS. 42A and 42B show a block diagram of the ASIC, and Table 1 belowprovides pad signal descriptions (shown on the left-hand side of FIGS.42A and 42B), with some signals being multiplexed onto a single pad.

TABLE 1 Pad signal descriptions Pad Name Functional Description Powerplane VBAT Battery power input 2.0 V to 4.5 V VBAT VDDBU Backup logicpower 1.4 to 2.4 V VDDBU VDD Logic power -- 1.6-2.4 V VDD VDDA Analogpower - 1.6-2.4 V VDDA VPAD Pad I/O power -- 1.8 V-3.3 V VPAD VSS Logicground return and digital pad return VSSA Analog ground return andanalog pad return ADC_IN1, 2 ADC Inputs, VDDA max input VDDA V1P2B 1.2volt reference Bypass capacitor VDDA nSHUTDN External VDD regulatorcontrol signal. Goes low when battery is VBAT low. VPAD_EN Goes highwhen VPAD IOs are active. Can control external VBAT regulator. DA1, 2DAC outputs VDDA TP_ANA_MUX Mux of analog test port -- output or inputVDDA TP_RES External 1 meg ohm calibration resistor & analog test portVDDA WORK1-5 Working Electrodes of Sensor VDDA RE Reference Electrode ofSensor VDDA COUNTER Counter Electrode of Sensor VDDA CMP1_IN Generalpurpose Voltage comparator VDDA CMP2_IN General purpose Voltagecomparator VDDA WAKEUP Debounced interrupt input VBAT XTALI, XTALO32.768 kHz Crystal Oscillator pads VDDA OSC_BYPASS Test clock controlVDDA SEN_CONN_SW Sensor connection switch input. Pulled to VSSA =connection VDDA VPAD_EN Enable the VPAD power and VPAD power plane logicVBAT nRESET_OD Signal to reset external circuitry such as amicroprocessor SPI_CK, SPI interface signals to microprocessor VPADnSPI_CS, SPI_MOIS, SPI_MISO UP_WAKEUP Microprocessor wakeup signal VPADCLK_32KHZ Gated Clock output to external circuitry microprocessor VPADUP_INT Interrupt signal to microprocessor VPAD nPOR1_OUT Backup Power onreset, output from analog VBAT nPOR1_IN VBAT power plane reset, input todigital in battery plane VBAT (VDDBU) nPOR2_OUT VDD POR signal, outputfrom analog VDD nPOR2_OUT_OD VDD POR signal open drain (nfet out only),stretched output VBAT from digital nPOR2_IN VDD power plane logic reset.Is level shifted to VDD inside the VDD chip, input to digital VDD logic.

The ASIC will now be described with reference to FIGS. 42A and 42B andTable 1.

Power Planes

The ASIC has one power plane that is powered by the supply pad VBAT(4210), which has an operating input range from 2.0 volts to 4.5 volts.This power plane has a regulator to lower the voltage for some circuitsin this plane. The supply is called VDDBU (4212) and has an output padfor test and bypassing. The circuits on the VBAT supply include an RCoscillator, real time clock (RC osc) 4214, battery protection circuit,regulator control, power on reset circuit (POR), and variousinputs/outputs. The pads on the VBAT power plane are configured to drawless than 75 nA at 40° C. and VBAT=3.50V.

The ASIC also has a VDD supply to supply logic. The VDD supply voltagerange is programmable from at least 1.6 volts to 2.4 volts. The circuitson the VDD power plane include most of the digital logic, timer (32khz), and real time clock (32 khz). The VDD supply plane includes levelshifters interfacing to the other voltage planes as necessary. The levelshifters, in turn, have interfaces conditioned so that any powered powerplane does not have an increase in current greater than 10 nA if anotherpower plane is unpowered.

The ASIC includes an onboard regulator (with shutdown control) and anoption for an external VDD source. The regulator input is a separatepad, REG_VDD_IN (4216), which has electrostatic discharge (ESD)protection in common with other I/Os on VBAT. The onboard regulator hasan output pad, REG_VDD_OUT (4217). The ASIC also has an input pad forthe VDD, which is separate from the REG_VDD_OUT pad.

The ASIC includes an analog power plane, called VDDA (4218), which ispowered by either the VDD onboard regulator or an external source, andis normally supplied by a filtered VDD. The VDDA supplied circuits areconfigured to operate within 0.1 volt of VDD, thereby obviating the needfor level shifting between the VDDA and VDD power planes. The VDDAsupply powers the sensor analog circuits, the analog measurementcircuits, as well as any other noise-sensitive circuitry.

The ASIC includes a pad supply, VPAD, for designated digital interfacesignals. The pad supply has an operating voltage range from at least 1.8V to 3.3 V. These pads have separate supply pad(s) and are powered froman external source. The pads also incorporate level shifters to otheronboard circuits to allow the flexible pad power supply rangeindependently of the VDD logic supply voltage. The ASIC can conditionthe VPAD pad ring signals such that, when the VPAD supply is notenabled, other supply currents will not increase by more than 10 nA.

Bias Generator

The ASIC has a bias generator circuit, BIAS_GEN (4220), which issupplied from the VBAT power, and which generates bias currents that arestable with supply voltage for the system. The output currents have thefollowing specifications: (i) Supply sensitivity: <±2.5% from a supplyvoltage of 1.6v to 4.5V; and (ii) Current accuracy: <±3% after trimming.

The BIAS_GEN circuit generates switched and unswitched output currentsto supply circuits needing a bias current for operation. The operatingcurrent drain of the BIAS_GEN circuit is less than 0.3 uA at 25° C. withVBAT from 2.5V-4.5V (excluding any bias output currents). Lastly, thetemperature coefficient of the bias current is generally between 4,000ppm/° C. and 6,000 ppm/° C.

Voltage Reference

The ASIC, as described herein is configured to have a low power voltagereference, which is powered from the VBAT power supply. The voltagereference has an enable input which can accept a signal from logicpowered by VBAT or VDDBU. The ASIC is designed such that the enablesignal does not cause any increase in current in excess of 10 nA fromany supply from this signal interface when VBAT is powered.

The reference voltage has the following specifications: (i) Outputvoltage: 1.220±3 mV after trimming; (ii) Supply sensitivity: <+6 mV from1.6 V to 4.5V input; (iii) Temperature sensitivity: <±5 mV from 0° C. to60° C.; and (iv) Output voltage default accuracy (without trim): 1.220V±50 mV. In addition, the supply current is to be less than 800 nA at4.5V, 40° C. In this embodiment, the reference output will be forced toVSSA when the reference is disabled so as to keep the VDD voltageregulator from overshooting to levels beyond the breakdown voltage ofthe logic.

32 kHz Oscillator

The ASIC includes a low power 32.768 kHz crystal oscillator 4222 whichis powered with power derived from the VDDA supply and can trim thecapacitance of the crystal oscillator pads (XTALI, XTALO) with software.Specifically, the frequency trim range is at least −50 ppm to +100 ppmwith a step size of 2 ppm max throughout the trim range. Here, a crystalmay be assumed with a load capacitance of 7 pF, Ls=6.9512 kH, Cs=3.3952fF, Rs=70 k, shunt capacitance=1 pF, and a PC Board parasiticcapacitance of 2 pF on each crystal terminal.

The ASIC has a VPAD level output available on a pad, CLK_32 kHZ, wherethe output can be disabled under software and logic control. The defaultis driving the 32 kHz oscillator out. An input pin, OSC32K_BYPASS(4224), can disable the 32 kHz oscillator (no power drain) and allowsfor digital input to the XTALI pad. The circuits associated with thisfunction are configured so as not to add any ASIC current in excess of10 nA in either state of the OSC32K_BYPASS signal other than theoscillator current when OSC32K_BYPASS is low.

The 32 kHZ oscillator is required to always be operational when the VDDAplane is powered, except for the bypass condition. If the OSC32K_BYPASSis true, the 32 KHZ oscillator analog circuitry is put into a low powerstate, and the XTALI pad is configured to accept a digital input whoselevel is from 0 to VDDA. It is noted that the 32 kHz oscillator outputhas a duty cycle between 40% and 60%.

Timer

The ASIC includes a Timer 4226 that is clocked from the 32 kHzoscillator divided by 2. It is pre-settable and has two programmabletimeouts. It has 24 programmable bits giving a total time count to 17minutes, 4 seconds. The Timer also has a programmable delay to disablethe clock to the CLK_32 KHz pad and set the microprocessor (uP)interface signals on the VPAD plane to a predetermined state (Seesection below on Microprocessor Wakeup Control Signals). This will allowthe microprocessor to go into suspend mode without an external clock.However, this function may be disabled by software with a programmablebit.

The Timer also includes a programmable delay to wakeup themicroprocessor by enabling the CLK_32 KHZ clock output and settingUP_WAKEUP high. A transition of the POR2 (VDD POR) from supply low stateto supply OK state will enable the 32 kHz oscillator, the CLK_32 KHZclock output and set UP_WAKEUP high. The power shutdown and power up areconfigured to be controlled with programmable control bits.

Real Time Clock (RTC)

The ASIC also has a 48 bit readable/writeable binary counter thatoperates from the ungated, free running 32 kHz oscillator. The write tothe real time clock 4228 requires a write to an address with a keybefore the clock can be written. The write access to the clock isconfigured to terminate between 1 msec and 20 msec after the write tothe key address.

The real time clock 4228 is configured to be reset by a power on reseteither by POR1_IN (the VBAT POR) or POR2_IN (the VDD_POR) to half count(MSB=1, all other bits 0). In embodiments of the invention, the realtime clock has programmable interrupt capability, and is designed to berobust against single event upsets (SEUs), which may be accomplishedeither by layout techniques or by adding capacitance to appropriatenodes, if required.

RC Oscillator

The ASIC further includes an RC clock powered from the VBAT supply orVBAT derived supply. The RC Oscillator is always running, except thatthe oscillator can be bypassed by writing to a register bit in analogtest mode (see section on Digital Testing) and applying a signal to theGPIO_VBAT with a 0 to VBAT level. The RC oscillator is not trimmable,and includes the following specifications: (i) a frequency between 750Hz and 1500 Hz; (ii) a duty cycle between 50%+10%; (iii) currentconsumption of less than 200 nA at 25° C.; (iv) frequency change of lessthan ±2% from 1V to 4.5V VBAT supply and better than 1% from 1.8V to4.5V VBAT supply; and (v) frequency change of less than +2, −2% from atemperature of 15° C. to 40° C. with VBAT=3.5V. The RC frequency can bemeasured with the 32 kHz crystal oscillator or with an externalfrequency source (See Oscillator Calibration Circuit).

Real Time RC Clock (RC oscillator based)

The ASIC includes a 48 bit readable/writeable binary ripple counterbased on the RC oscillator. A write to the RC real time clock requires awrite to an address with a key before the clock can be written. Thewrite access to the clock terminates between 1 msec and 20 msec afterthe write to the key address, wherein the time for the protection windowis configured to be generated with the RC clock.

The real time RC clock allows for a relative time stamp if the crystaloscillator is shutdown, and is configured to be reset on POR1_IN (theBAT POR) to half count (MSB=1, all others 0). The real time RC clock isdesigned to be robust against single event upsets (SEUs) either bylayout techniques or by adding capacitance to appropriate nodes, whererequired. On the falling edge of POR2_IN, or if the ASIC goes intoBattery Low state, the RT real time clock value may be captured into aregister that can be read via the SPI port. This register and associatedlogic are on the VBAT or VDDBU power plane.

Battery Protection Circuit

The ASIC includes a battery protection circuit 4230 that uses acomparator to monitor the battery voltage and is powered with powerderived from the VBAT power plane. The battery protection circuit isconfigured to be always running with power applied to the VBAT supply.The battery protection circuit may use the RC oscillator for clockingsignals, and have an average current drain that is less than 30 nA,including a 3 MOhm total resistance external voltage divider.

The battery protection circuit uses an external switched voltage dividerhaving a ratio of 0.421 for a 2.90V battery threshold. The ASIC also hasan internal voltage divider with the ratio of 0.421±0.5%. This divideris connected between BATT_DIV_EN (4232) and VSSA (4234), and the divideroutput is a pin called BATT_DIV_INT (4236). To save pins in the packagedpart, the BATT_DIV_INT in this embodiment is connected to BATT_DIVinternally in the package. Also in this configuration, BATT_DIV_EN doesnot need to come out of the package, saving two package pins.

The battery protection circuit is configured to sample the voltage on aninput pin, BATT_DIV (4238), at approximately 2 times per second, whereinthe sample time is generated from the RC Oscillator. The ASIC is able toadjust the divider of the RC Oscillator to adjust the sampling timeinterval to 0.500 sec±5 msec with the RC oscillator operating within itsoperating tolerance. In a preferred embodiment, the ASIC has a test modewhich allows more frequent sampling intervals during test.

The comparator input is configured to accept an input from 0 to VBATvolts. The input current to the comparator input, BATT_DIV, is less than10 nA for inputs from 0 to VBAT volts. The comparator sampling circuitoutputs to a pad, BATT_DIV_EN, a positive pulse which can be used byexternal circuitry to enable an off-chip resistor divider only duringthe sampling time to save power. The voltage high logic level is theVBAT voltage and the low level is VSS level.

The output resistance of the BATT_DIV_EN pad shall be less than 2 kOhmsat VBAT=3.0V. This allows the voltage divider to be driven directly fromthis output. After a programmable number of consecutive samplesindicating a low battery condition, the comparator control circuitrytriggers an interrupt to the interrupt output pad, UP_INT. The defaultnumber of samples is 4, although the number of consecutive samples isprogrammable from 4 to 120.

After a programmable number of consecutive samples indicating a lowbattery after the generation of the UP_INT above, the comparator controlcircuitry is configured to generate signals that will put the ASIC intoa low power mode: The VDD regulator will be disabled and a low signalwill be asserted to the pad, VPAD_EN. This will be called the BatteryLow state. Again, the number of consecutive samples is programmable from4 to 120 samples, with the default being 4 samples.

The comparator has individual programmable thresholds for falling andrising voltages on BATT_DIV. This is implemented in the digital logic tomultiplex the two values to the circuit depending on the state of theBattery Low state. Thus, if Battery Low state is low, the fallingthreshold applies, and if the Battery Low state is high, the risingthreshold applies. Specifically, the comparator has 16 programmablethresholds from 1.22 to 1.645±3%, wherein the DNL of the programmablethresholds is set to be less than 0.2 LSB.

The comparator threshold varies less than +/−1% from 20° C. to 40° C.The default threshold for falling voltage is 1.44V (VBAT threshold of3.41V with nominal voltage divider), and the default threshold forrising voltage is 1.53V (VBAT threshold of 3.63V with nominal voltagedivider). After the ASIC has been put into the Battery Low state, if thecomparator senses 4 consecutive indications of battery OK, then the ASICwill initiate the microprocessor startup sequence.

Battery Power Plane Power On Reset

A power on reset (POR) output is generated on pad nPOR1_OUT (4240) ifthe input VBAT slews more than 1.2 volt in a 50 usec period or if theVBAT voltage is below 1.6±0.3 volts. This POR is stretched to a minimumpulse width of 5 milliseconds. The output of the POR circuit isconfigured to be active low and go to a pad, nPOR1_OUT, on the VBATpower plane.

The IC has an input pad for the battery power plane POR, nPOR1_IN(4242). This input pad has RC filtering such that pulses shorter than 50nsec will not cause a reset to the logic. In this embodiment, nPOR1_OUTis externally connected to the nPOR1_IN in normal operation, therebyseparating the analog circuitry from the digital circuitry for testing.The nPOR1_IN causes a reset of all logic on any of the power planes, andinitializes all registers to their default value. Thus, the reset statusregister POR bit is set, and all other reset status register bits arecleared. The POR reset circuitry is configured so as not to consume morethan 0.1 uA from VBAT supply for time greater than 5 seconds after powerup.

VDD Power on Reset (POR)

The ASIC also has a voltage comparator circuit which generates a VDDvoltage plane reset signal upon power up, or if the VDD drops below aprogrammable threshold. The range is programmable with several voltagethresholds. The default value is 1.8V−15% (1.53V). The POR2 has aprogrammable threshold for rising voltage, which implements hysteresis.The rising threshold is also programmable, with a default value of1.60V±3%.

The POR signal is active low and has an output pad, nPOR2_OUT (4244), onthe VDD power plane. The ASIC also has an active low POR open drainoutput, nPOR2_OUT_OD (4246), on the VBAT power plane. This could be usedfor applying POR to other system components.

The VDD powered logic has POR derived from the input pad, nPOR2_IN(4248). The nPOR2_IN pad is on the VDD power plane, and has RC filteringsuch that pulses shorter than 50 nsec will not cause a reset to thelogic. The nPOR2_OUT is configured be externally connected to thenPOR2_IN input pad under normal usage, thereby separating the analogcircuitry from the digital circuitry.

The reset which is generated is stretched to at least 700 msec of activetime after VDD goes above the programmable threshold to assure that thecrystal oscillator is stable. The POR reset circuitry is to consume nomore than 0.1 uA from the VDD supply for time greater than 5 secondsafter power up, and no more than 0.1 uA from VBAT supply for timegreater than 5 seconds after power up. The register that stores the PORthreshold value is powered from the VDD power plane.

Sensor Interface Electronics

In embodiments of the inventions described herein, the sensor circuitrysupports up to five sensor WORK electrodes (4310) in any combination ofperoxide or oxygen sensors, although, in additional embodiments, alarger number of such electrodes may also be accommodated. While theperoxide sensor WORK electrodes source current, the oxygen sensor WORKelectrodes sink current. For the instant embodiment, the sensors can beconfigured in the potentiostat configuration as shown in FIG. 43.

The sensor electronics have programmable power controls for eachelectrode interface circuit to minimize current drain by turning offcurrent to unused sensor electronics. The sensor electronics alsoinclude electronics to drive a COUNTER electrode 4320 that uses feedbackfrom a RE (reference) electrode 4330. The current to this circuitry maybe programmed off when not in use to conserve power. The interfaceelectronics include a multiplexer 4250 so that the COUNTER and REelectrodes may be connected to any of the (redundant) WORK electrodes.

The ASIC is configured to provide the following Sensor Interfaces: (i)RE: Reference electrode, which establishes a reference potential of thesolution for the electronics for setting the WORK voltages; (ii)WORK1-WORK5: Working sensor electrodes where desired reduction/oxidation(redox) reactions take place; and (iii) COUNTER: Output from this padmaintains a known voltage on the RE electrode relative to the systemVSS. In this embodiment, the ASIC is configured so as to be able toindividually set the WORK voltages for up to 5 WORK electrodes with aresolution and accuracy of better than or equal to 5 mV.

The WORK voltage(s) are programmable between at least 0 and 1.22Vrelative to VSSA in the oxygen mode. In the peroxide mode, the WORKvoltage(s) are programmable between at least 0.6 volt and 2.054 voltsrelative to VSSA. If the VDDA is less than 2.15V, the WORK voltage isoperational to VDDA−0.1V. The ASIC includes current measuring circuitsto measure the WORK electrode currents in the peroxide sensor mode. Thismay be implemented, e.g., with current-to-voltage orcurrent-to-frequency converters, which may have the followingspecifications: (i) Current Range: 0-300 nA; (ii) Voltage output range:Same as WORK electrode in peroxide/oxygen mode; (iii) Output offsetvoltage: ±5 mV max; and (iv) Uncalibrated resolution: ±0.25 nA.

Current Measurement Accuracy after applying a calibration factor to thegain and assuming an acquisition time of 10 seconds or less is:

-   -   5 pA-nA: ±3%±20 pA    -   1 nA-10 nA: ±3%±20 pA    -   10 nA-300 nA: ±3%±0.2 nA

For current-to-frequency converters (ItoFs) only, the frequency rangemay be between 0 Hz and 50 kHz. The current converters must operate inthe specified voltage range relative to VSS of WORK electrodes in theperoxide mode. Here, the current drain is less than 2 uA from a 2.5Vsupply with WORK electrode current less than 10 nA per converterincluding digital-to-analog (DAC) current.

The current converters can be enabled or disabled by software control.When disabled, the WORK electrode will exhibit a very high impedancevalue, i.e., greater than 100 Mohm. Again, for ItoFs only, the output ofthe I-to-F converters will go to 32 bit counters, which can be read,written to, and cleared by the microprocessor and test logic. During acounter read, clocking of the counter is suspended to ensure an accurateread.

In embodiments of the inventions described herein, the ASIC alsoincludes current measuring circuits to measure the WORK electrodecurrents in the oxygen sensor mode. The circuit may be implemented as acurrent-to-voltage or a current-to-frequency converter, and aprogrammable bit may be used to configure the current converters tooperate in the oxygen mode. As before, the current converters mustoperate in the specified voltage range of the WORK electrodes relativeto VSS in the oxygen mode. Here, again, the current range is 3.7 pA-300nA, the voltage output range is the same as WORK electrode in oxygenmode, the output offset voltage is ±5 mV max, and the uncalibratedresolution is 3.7 pA±2 pA.

Current Measurement Accuracy after applying a calibration factor to thegain and assuming an acquisition time of 10 seconds or less is:

-   -   5 pA-1 nA: ±3%±20 pA    -   1 nA-10 nA: ±3%±20 pA    -   10 nA-300 nA: ±3%±0.2 nA

For current-to-frequency converters (ItoFs) only, the frequency rangemay be between 0 Hz and 50 kHz, and the current drain is less than 2 uAfrom a 2.5V supply with WORK electrode current less than 10 nA perconverter, including DAC current. The current converters can be enabledor disabled by software control. When disabled, the WORK electrode willexhibit a very high impedance value, i.e., greater than 100 Mohm. Also,for ItoFs only, the output of the I-to-F converters will go to 32 bitcounters, which can be read, written to, and cleared by themicroprocessor and test logic. During a counter read, clocking of thecounter is suspended to ensure an accurate read.

In embodiments of the inventions described herein, the Referenceelectrode (RE) 4330 has an input bias current of less than 0.05 nA at40° C. The COUNTER electrode adjusts its output to maintain a desiredvoltage on the RE electrode. This is accomplished with an amplifier 4340whose output to the COUNTER electrode 4320 attempts to minimize thedifference between the actual RE electrode voltage and the target REvoltage, the latter being set by a DAC.

The RE set voltage is programmable between at least 0 and 1.80V, and thecommon mode input range of the COUNTER amplifier includes at least 0.20to (VDD−0.20)V. A register bit may be used to select the common modeinput range, if necessary, and to provide for programming the mode ofoperation of the COUNTER. The WORK voltage is set with a resolution andaccuracy of better than or equal to 5 mV. It is noted that, in thenormal mode, the COUNTER voltage seeks a level that maintains the REvoltage to the programmed RE target value. In the force counter mode,however, the COUNTER electrode voltage is forced to the programmed REtarget voltage.

All electrode driving circuits are configured to be able to drive theelectrode to electrode load and be free from oscillation for any usescenario. FIG. 44 shows the equivalent ac inter-electrode circuitaccording to an embodiment with the potentiostat configuration as shownin FIG. 43. The equivalent circuit shown in FIG. 44 may be between anyof the electrodes, i.e., WORK1-WORK5, COUNTER and RE, with value rangesas follows for the respective circuit components:

-   -   Ru=[200-5 k] Ohms    -   Cc=[10-2000] pF    -   Rpo=[1-20] kOhms    -   Rf=[200-2000] kOhms    -   Cf=[2-30] uF

During initialization, the drive current for WORK electrodes and theCOUNTER electrode need to supply higher currents than for the normalpotentiostat operation described previously. As such, programmableregister bits may be used to program the electrode drive circuits to ahigher power state if necessary for extra drive. It is important toachieve low power operation in the normal potentiostat mode, where theelectrode currents are typically less than 300 nA.

In preferred embodiments, during initialization, the WORK1 through WORK5electrodes are programmable in steps equal to, or less than, 5 mV from 0to VDD volts, and their drive or sink current output capability is aminimum of 20 uA, from 0.20V to (VDD−0.20V). Also during initialization,the ASIC is generally configured to be able to measure the current ofone WORK electrode up to 20 uA with an accuracy of ±2%±40 nA of themeasurement value. Moreover, during initialization, the RE set voltageis programmable as described previously, the COUNTER DRIVE CIRCUIToutput must be able to source or sink 50 uA minimum with the COUNTERelectrode from 0.20V to (VDD−0.20V), and the supply current (VDD andVDDA) to the initialization circuitry is required to be less than 50 uAin excess of any output current sourced.

Current Calibrator

In embodiments of the invention, the ASIC has a current reference thatcan be steered to any WORK electrode for the purpose of calibration. Inthis regard, the calibrator includes a programmable bit that causes thecurrent output to sink current or source current. The programmablecurrents include at least 10 nA, 100 nA, and 300 nA, with an accuracy ofbetter than ±1%+1 nA, assuming a 0 tolerance external precisionresistor. The calibrator uses a 1 MegOhm precision resistor connected tothe pad, TP_RES (4260), for a reference resistance. In addition, thecurrent reference can be steered to the COUNTER or RE electrodes for thepurpose of initialization and/or sensor status. A constant current maybe applied to the COUNTER or the RE electrodes and the electrode voltagemay be measured with the ADC.

High Speed RC Oscillator

With reference back to FIG. 42, the ASIC further includes a high speedRC oscillator 4262 which supplies the analog-to-digital converter (ADC)4264, the ADC sequencer 4266, and other digital functions requiring ahigher speed clock than 32 kHz. The high speed RC oscillator is phasedlocked to the 32 kHz clock (32.768 kHz) to give an output frequencyprogrammable from 524.3 kHz to 1048 kHz. In addition, the high speed RCoscillator has a duty cycle of 50%±10%, a phase jitter of less than 0.5%rms, a current of less than 10 uA, and a frequency that is stablethrough the VDD operating range (voltage range of 1.6 to 2.5V). Thedefault of the high speed RC oscillator is “off” (i.e., disabled), inwhich case the current draw is less than 10 nA. However, the ASIC has aprogrammable bit to enable the High Speed RC oscillator.

Analog to Digital Converter

The ASIC includes a 12-bit ADC (4264) with the followingcharacteristics: (i) capability to effect a conversion in less than 1.5msec with running from a 32 kHz clock; (ii) ability to perform fasterconversions when clocked from the high speed RC oscillator; (iii) haveat least 10 bits of accuracy (12 bit±4 counts); (iv) have a referencevoltage input of 1.220V, with a temperature sensitivity of less than 0.2mV/° C. from 20° C. to 40° C.; (v) full scale input ranges of 0 to1.22V, 0 to 1.774V, 0 to 2.44V, and 0−VDDA, wherein the 1.774 and 2.44Vranges have programmable bits to reduce the conversion range to lowervalues to accommodate lower VDDA voltages; (vi) have current consumptionof less than 50 uA from its power supply; (vi) have a converter capableof operating from the 32 kHz clock or the High Speed RC clock; (vii)have a DNL of less than 1 LSB; and (viii) issue an interrupt at the endof a conversion.

As shown in FIGS. 42A and 42B, the ASIC has an analog multiplexer 4268at the input of the ADC 4264, both of which are controllable bysoftware. In a preferred embodiment, at least the following signals areconnected to the multiplexer:

-   -   (i) VDD—Core Voltage and regulator output    -   (ii) VBAT—Battery source    -   (iii) VDDA—Analog supply    -   (iv) RE—Reference Electrode of Sensor    -   (v) COUNTER—Counter Electrode of Sensor    -   (vi) WORK1-WORK5—Working Electrodes of Sensor    -   (vii) Temperature sensor    -   (viii) At least two external pin analog signal inputs    -   (ix) EIS integrator outputs    -   (x) ItoV current converter output.

The ASIC is configured such that the loading of the ADC will not exceed±0.01 nA for the inputs COUNTER, RE, WORK1-WORK5, the temperaturesensor, and any other input that would be adversely affected by loading.The multiplexer includes a divider for any inputs that have highervoltage than the input voltage range of the ADC, and a buffer amplifierthat will decrease the input resistance of the divided inputs to lessthan 1 nA for load sensitive inputs. The buffer amplifier, in turn, hasa common mode input range from at least 0.8V to VDDA voltage, and anoffset less than 3 mV from the input range from 0.8V to VDDA-0.1V.

In a preferred embodiment, the ASIC has a mode where the ADCmeasurements are taken in a programmed sequence. Thus, the ASIC includesa programmable sequencer 4266 that supervises the measurement of up to 8input sources for ADC measurements with the following programmableparameters:

-   -   (i) ADC MUX input    -   (ii) ADC range    -   (iii) Delay time before measurement, wherein the delays are        programmable from 0 to 62 msec in 0.488 msec steps    -   (iv) Number of measurements for each input from 0 to 255    -   (v) Number of cycles of measurements: 0-255, wherein the cycle        of measurements refers to repeating the sequence of up to 8        input measurements multiple times (e.g., as an outer loop in a        program)    -   (vi) Delay between cycles of measurement, wherein the delays are        programmable from 0 to 62 msec in 0.488 msec steps.

The sequencer 4266 is configured to start upon receiving an auto-measurestart command, and the measurements may be stored in the ASIC forretrieval over the SPI interface. It is noted that the sequencer timebase is programmable between the 32 kHz clock and the High Speed RCoscillator 4262.

Sensor Diagnostics

As was previously described in detail, embodiments of the inventionsdescribed herein are directed to the use of impedance andimpedance-related parameters in, e.g., sensor diagnostic procedures andIsig/SG fusion algorithms. To that end, in preferred embodiments, theASIC described herein has the capability of measuring the impedancemagnitude and phase angle of any WORK sensor electrode to the RE andCOUNTER electrode when in the potentiostat configuration. This is done,e.g., by measuring the amplitude and phase of the current waveform inresponse to a sine-like waveform superimposed on the WORK electrodevoltage. See, e.g., Diagnostic Circuitry 4255 in FIG. 42B.

The ASIC has the capability of measuring the resistive and capacitivecomponents of any electrode to any electrode via, e.g., the ElectrodeMultiplexer 4250. It is noted that such measurements may interfere withthe sensor equilibrium and may require settling time or sensorinitialization to record stable electrode currents. As discussedpreviously, although the ASIC may be used for impedance measurementsacross a wide spectrum of frequencies, for purposes of the embodimentsof the inventions, a relatively narrower frequency range may be used.Specifically, the ASIC's sine wave measurement capability may includetest frequencies from about 0.10 Hz to about 8192 Hz. In making suchmeasurements, the minimum frequency resolution in accordance with anembodiment of the invention may be limited as shown in Table 2 below:

TABLE 2 Frequency [Hz] Min step [Hz] .1 to 15 <1 16 to 31 1 32 to 63 264 to 127 4 128 to 255 8 256 to 511 16 512 to 1023 32 1024 to 2047 642048 to 4095 128 4096 to 8192 256

The sinewave amplitude is programmable from at least 10 mVp-p to 50mVp-p in 5 mV steps, and from 60 mVp-p to 100 mVp-p in 10 mV steps. In apreferred embodiment, the amplitude accuracy is better than ±5% or ±5mV, whichever is larger. In addition, the ASIC may measure the electrodeimpedance with accuracies specified in Table 3 below:

TABLE 3 Impedance Phase Measurement Measurement Frequency RangeImpedance Range Accuracy Accuracy .1-10 Hz 2k to 1 MegΩ ±5% ±0.5° 10-100Hz 1k to 100 kΩ ±5% ±0.5° 100 to 8000 Hz .5k to 20 kΩ ±5% ±1.0°

In an embodiment of the invention, the ASIC can measure the inputwaveform phase relative to a time base, which can be used in theimpedance calculations to increase the accuracy. The ASIC may also haveon-chip resistors to calibrate the above electrode impedance circuit.The on-chip resistors, in turn, may be calibrated by comparing them tothe known 1 MegOhm off-chip precision resistor.

Data sampling of the waveforms may also be used to determine theimpedances. The data may be transmitted to an external microprocessorwith the serial peripheral interface (SPI) for calculation andprocessing. The converted current data is sufficiently buffered to beable to transfer 2000 ADC conversions of data to an external devicethrough the SPI interface without losing data. This assumes a latencytime of 8 msec maximum for servicing a data transfer request interrupt.

In embodiments of the invention, rather than, or in addition to,measuring electrode impedance with a sine wave, the ASIC may measureelectrode current with a step input. Here, the ASIC can supplyprogrammable amplitude steps from 10 to 200 mV with better than 5 mVresolution to an electrode and sample (measure) the resulting currentwaveform. The duration of the sampling may be programmable to at least 2seconds in 0.25 second steps, and the sampling interval for measuringcurrent may include at least five programmable binary weighted stepsapproximately 0.5 msec to 8 msec.

The resolution of the electrode voltage samples is smaller than 1 mVwith a range up to ±0.25 volts. This measurement can be with respect toa suitable stable voltage in order to reduce the required dynamic rangeof the data conversion. Similarly, the resolution of the electrodecurrent samples is smaller than 0.04 uA with a range up to 20 uA. Thecurrent measurements can be unipolar if the measurement polarity isprogrammable.

In embodiments of the invention, the current measurement may use anI-to-V converter. Moreover, the ASIC may have on-chip resistors tocalibrate the current measurement. The on-chip resistors, in turn, maybe calibrated by comparing them to the known 1 MegOhm off-chip precisionresistor. The current measurement sample accuracy is better than ±3% or10 nA, whichever is greater. As before, the converted current data issufficiently buffered to be able to transfer 2000 ADC conversions ofdata to an external device through the SPI interface without losingdata. This assumes a latency time of 8 msec maximum for servicing a datatransfer request interrupt.

Calibration Voltage

The ASIC includes a precision voltage reference to calibrate the ADC.The output voltage is 1.000V±3% with less than ±1.5% variation inproduction, and stability is better than ±3 mV over a temperature rangeof 20° C. to 40° C. This precision calibration voltage may becalibrated, via the on-chip ADC, by comparing it to an externalprecision voltage during manufacture. In manufacturing, a calibrationfactor may be stored in a system non-volatile memory (not on this ASIC)to achieve higher accuracy.

The current drain of the calibration voltage circuit is preferably lessthan 25 uA. Moreover, the calibration voltage circuit is able to powerdown to less than 10 nA to conserve battery power when not in use.

Temperature Sensor

The ASIC has a temperature transducer having a sensitivity between 9 and11 mV per degree Celsius between the range −10° C. to 60° C. The outputvoltage of the Temperature Sensor is such that the ADC can measure thetemperature-related voltage with the 0 to 1.22V ADC input range. Thecurrent drain of the Temperature Sensor is preferably less than 25 uA,and the Temperature Sensor can power down to less than 10 nA to conservebattery power when not in use.

VDD Voltage Regulator

The ASIC has a VDD voltage regulator with the following characteristics:

-   -   (i) Minimum input Voltage Range: 2.0V-4.5V.    -   (ii) Minimum output Voltage: 1.6-2.5V±5%, with a default of        2.0V.    -   (iii) Dropout voltage: Vin−Vout<0.15V at Iload=100 uA, Vin=2.0V.    -   (iv) The output voltage is programmable, with an accuracy within        2% of the indicated value per Table 4 below:

TABLE 4 Hex vout hex vout 0 1.427 10 1.964 1 1.460 11 1.998 2 1.494 122.032 3 1.528 13 2.065 4 1.561 14 2.099 5 1.595 15 2.132 6 1.628 162.166 7 1.662 17 2.200 8 1.696 18 2.233 9 1.729 19 2.267 A 1.763 1A2.300 B 1.796 1B 2.334 C 1.830 1C 2.368 D 1.864 1D 2.401 E 1.897 1E2.435 F 1.931 1F  2.468

-   -   (v) The regulator can supply output of 1 mA at 2.5V with an        input voltage of 2.8V.    -   (vi) The regulator also has input and output pads that may be        open circuited if an external regulator is used. The current        draw of the regulator circuit is preferably less than 100 nA in        this non-operational mode.    -   (vii) The change of output voltage from a load of 10 uA to 1 mA        is preferably less than 25 mV.    -   (viii) Current Drain excluding output current @ 1 mA load is        less than 100 uA from source.    -   (ix) Current Drain excluding output current @ 0.1 mA load is        less than 10 uA from source.    -   (x) Current Drain excluding output current @ 10 uA load is less        than 1 uA from source.

General Purpose Comparators

The ASIC includes at least two comparators 4270, 4271 powered from VDDA.The comparators use 1.22V as a reference to generate the threshold. Theoutput of the comparators can be read by the processor and will create amaskable interrupt on the rising or falling edge determined byconfiguration registers.

The comparators have power control to reduce power when not in use, andthe current supply is less than 50 nA per comparator. The response timeof the comparator is preferably less than 50 usec for a 20 mV overdrivesignal, and the offset voltage is less than ±8 mV.

The comparators also have programmable hysteresis, wherein thehysteresis options include threshold=1.22V+Vhyst on a rising input,threshold=1.22−Vhyst on a falling input, or no hysteresis (Vhyst=25±10mV). The output from either comparator is available to any GPIO on anypower plane. (See GPIO section).

Sensor Connection Sensing Circuitry on RE

An analog switched capacitor circuit monitors the impedance of the REconnection to determine if the sensor is connected. Specifically, acapacitor of about 20 pF is switched at a frequency of 16 Hz driven byan inverter with an output swing from VSS to VDD. Comparators will sensethe voltage swing on the RE pad and, if the swing is less than athreshold, the comparator output will indicate a connection. Theabove-mentioned comparisons are made on both transitions of the pulse. Aswing below threshold on both transitions is required to indicate aconnect, and a comparison indicating high swing on either phase willindicate a disconnect. The connect signal/disconnect signal is debouncedsuch that a transition of its state requires a stable indication to thenew state for at least ½ second.

The circuit has six thresholds defined by the following resistances inparallel with a 20 pF capacitor: 500 k, 1 Meg, 2 MEG, 4 Meg, 8 Meg, and16 Meg ohms. This parallel equivalent circuit is between the RE pad anda virtual ground that can be at any voltage between the power rails. Thethreshold accuracy is better than ±30%.

The output of the Sensor Connect sensing circuitry is able toprogrammably generate an interrupt or processor startup if a sensor isconnected or disconnected. This circuit is active whenever the nPOR2_INis high and the VDD and VDDA are present. The current drain for thiscircuit is less than 100 nA average.

WAKEUP Pad

The WAKEUP circuitry is powered by the VDD supply, with an input havinga range from 0V to VBAT. The WAKEUP pad 4272 has a weak pulldown of80±40 nA. This current can be derived from an output of the BIAS_GEN4220. The average current consumed by the circuit is less than 50 nAwith 0 v input.

The WAKEUP input has a rising input voltage threshold, Vih, of 1.22±0.1V, and the falling input threshold is −25 mV±12 mV that of the risingthreshold. In preferred embodiments, the circuit associated with theWAKEUP input draws no more than 100 nA for any input whose value is from−0.2 to VBAT voltage (this current excludes the input pulldown current).The WAKEUP pad is debounced for at least ½ second.

The output of the WAKEUP circuit is able to programmably generate aninterrupt or processor startup if the WAKEUP pad changes state. (See theEvent Handler section). It is important to note that the WAKEUP padcircuitry is configured to assume a low current, <1 nA, if the BatteryProtection Circuit indicates a low battery state.

UART WAKEUP

The ASIC is configured to monitor the nRX_EXT pad 4274. If the nRX_EXTlevel is continuously high (UART BREAK) for longer than ½ second, a UARTWAKEUP event will be generated. The due to sampling the UART WAKEUPevent could be generated with a continuous high as short as ¼ second.The UART WAKEUP event can programmably generate an interrupt, WAKEUPand/or a microprocessor reset (nRESET_OD). (See the Event Handlersection).

In preferred embodiments, the circuit associated with the UART WAKEUPinput draws no more than 100 nA, and the UART WAKEUP pad circuitry isconfigured to assume a low current, <1 nA, if the Battery Protectioncircuitry indicates a Battery Low state. The UART Wakeup input has arising input voltage threshold, Vih, of 1.22±0.1 V. The falling inputthreshold is −25 mV±12 mV that of the rising threshold.

Microprocessor Wakeup Control Signals

The ASIC is able to generate signals to help control the powermanagement of a microprocessor. Specifically, the ASIC may generate thefollowing signals:

-   -   (i) nSHUTDN—nSHUTDN may control the power enable of an off chip        VDD regulator. The nSHUTDN pad is on the VBAT power rail.        nSHUTDN shall be low if the Battery Protection circuitry        indicates a Battery Low state, otherwise nSHUTDN shall be high.    -   (ii) VPAD_EN—VPAD_EN may control the power enable of an external        regulator that supplies VPAD power. An internal signal that        corresponds to this external signal ensures that inputs from the        VPAD pads will not cause extra current due to floating inputs        when the VPAD power is disabled. The VPAD_EN pad is an output on        the VBAT power rail. The VPAD_EN signal is low if the Battery        Protection signal indicates a low battery. The VPAD_EN signal        may be set low by a software command that starts a timer; the        terminal count of the timer forces VPAD_EN low. The following        events may cause the VPAD_EN signal to go high if the Battery        Protection signal indicates a good battery (see Event Handler        for more details): nPOR2_IN transitioning from low to high;        SW/Timer (programmable); WAKEUP transition; low to high, and/or        high to low, (programmable); Sensor Connect transition; low to        high, and/or high to low, (programmable); UART Break; and RTC        Time Event (programmable).    -   (iii) UP_WAKEUP—UP_WAKEUP may connect to a microprocessor wakeup        pad. It is intended to wakeup the microprocessor from a sleep        mode or similar power down mode. The UP_WAKEUP pad is an output        on the VPAD power rail. The UP_WAKEUP signal can be programmed        to be active low, active high or a pulse. The UP_WAKEUP signal        may be set low by a software command that starts a timer; the        terminal count of the timer forces UP_WAKEUP low. The following        events may cause the UP_WAKEUP signal to go high if the Battery        Protection signal indicates a good battery (see Event Handler        for more details): nPOR2_IN transitioning from low to high;        SW/Timer (programmable); WAKEUP transition; low to high, and/or        high to low, (programmable); Sensor Connect transition; low to        high, and/or high to low, (programmable); UART Break; and RTC        Time Event (programmable). The WAKEUP signal may be delayed by a        programmable amount. If WAKEUP is programmed to be a pulse, the        pulse width may be programmed.    -   (iv) CLK_32 KHZ—CLK_32 KHZ pad may connect to a microprocessor        to supply a low speed clock. The clock is on-off programmable        and programmably turns on to wakeup events. The CLK_32 KHZ pad        is an output on the VPAD power rail. The CLK_32 KHZ signal is        low if the Battery Protection signal indicates a low battery.        The CLK_32 KHZ output may be programmed off by a programmable        bit. The default is ON. The CLK_32 KHZ signal may be disabled by        a software command that starts a timer; The terminal count of        the timer forces CLK_32 KHZ low. The following events may cause        the CLK_32 KHZ signal to be enabled if the Battery Protection        signal indicates a good battery (see Event Handler for more        details): nPOR2_IN transitioning from low to high; SW/Timer        (programmable); WAKEUP transition; low to high, and/or high to        low, (programmable); Sensor Connect transition; low to high,        and/or high to low, (programmable); UART Break; RTC Time Event        (programmable); and Detection of low battery by Battery        Protection Circuit.    -   (v) nRESET_OD—nRESET_OD may connect to a microprocessor to cause        a microprocessor reset. The nRESET_OD is programmable to wakeup        events. The nRESET_OD pad is an output on the VPAD power rail.        This pad is open drain (nfet output). The nRESET_OD signal is        low if the Battery Protection signal indicates a low battery.        The nRESET_OD active time is programmable from 1 to 200 msec.        The default is 200 ms. The following events may cause the        nRESET_OD signal to be asserted low (see Event Handler for more        details): nPOR2_IN; SW/Timer (programmable); WAKEUP transition;        low to high, and/or high to low, (programmable); Sensor Connect        transition; low to high, and/or high to low, (programmable);        UART Break; and RTC Time Event (programmable).    -   (vi) UP_INT—UP_INT may connect to a microprocessor to        communicate interrupts. The UP_INT is programmable to wakeup        events. The UP_INT pad is an output on the VPAD power rail. The        UP_INT signal is low if the Battery Protection signal indicates        a low battery. The UP_INT signal may be set high by a software        command that starts a timer; the terminal count of the timer        forces UP_INT high. The following events may cause the UP_INT        signal to be asserted high if the Battery Protection signal        indicates a good battery (see Event Handler for more details):        SW/Timer (programmable); WAKEUP transition; low to high, and/or        high to low, (programmable); Sensor Connect transition; low to        high and/or high to low, (programmable); UART Break; RTC Time        Event (programmable); Detection of low battery by Battery        Protection Circuit; and any of the ASIC interrupts when        unmasked.

The ASIC has GPIO1 and GPIO0 pads able to act as boot mode control for amicroprocessor. A POR2 event will reset a 2 bit counter whose bits mapto GPIO1 & GPIO0 (MSB, LSB respectively). A rising edge of UART breakincrements the counter by one, wherein the counter counts by modulo 4,and goes to zero if it is incremented in state 11. The boot mode counteris pre-settable via SPI.

Event Handler/Watchdog

The ASIC incorporates an event handler to define the responses toevents, including changes in system states and input signals. Eventsinclude all sources of interrupts (e.g. UART_BRK, WAKE_UP, SensorConnect, etc. . . . ). The event handler responses to stimuli areprogrammable by the software through the SPI interface. Some responses,however, may be hardwired (non-programmable).

The event handler actions include enable/disable VPAD_EN, enable/disableCLK_32 KHZ, assert nRESET_OD, assert UP_WAKEUP, and assert UP_INT. TheEvent Watchdog Timer 1 through Timer 5 are individually programmable in250 msec increments from 250 msec to 16,384 seconds. The timeouts forEvent Watchdog timers 6 through 8 are hardcoded. The timeout for Timer6and Timer7 are 1 minute; timeout for Timer8 is 5 minutes.

The ASIC also has a watchdog function to monitor the microprocessor'sresponses when triggered by an event. The event watchdog is activatedwhen the microprocessor fails to acknowledge the event inducedactivities. The event watchdog, once activated, performs a programmablesequence of actions, Event Watchdog Timer 1-5, and followed by ahard-wired sequence of actions, Event Watchdog Timer 6-8, to re-gain theresponse of the microprocessor. The sequence of actions includesinterrupt, reset, wake up, assert 32 KHz clock, power down and power upto the microprocessor.

During the sequences of actions, if the microprocessor regains itsability to acknowledge the activities that had been recorded, the eventwatchdog is reset. If the ASIC fails to obtain an acknowledgement fromthe microprocessor, the event watchdog powers down the microprocessor ina condition that will allow UART_BRK to reboot the microprocessor and itwill activate the alarm. When activated, the alarm condition generates asquare wave with a frequency of approximately 1 kHz on the pad ALARMwith a programmable repeating pattern. The programmable pattern has twoprogrammable sequences with programmable burst on and off times. Thealarm has another programmable pattern that may be programmed via theSPI port. It will have two programmable sequences with programmableburst on and off times.

Digital to Analog (D/A)

In a preferred embodiment, the ASIC has two 8 bit D/A converters 4276,4278 with the following characteristics:

-   -   (i) The D/A settles in less than 1 msec with less than 50 pF        load.    -   (ii) The D/A has at least 8 bits of accuracy.    -   (iii) The output range is programmable to either 0 to 1.22V or 0        to VDDA.    -   (iv) Temperature sensitivity of the D/A voltage reference is        less than 1 mV/° C.    -   (v) The DNL is less than 1 LSB.    -   (vi) Current consumed by the D/A is less than 2 uA from the VDDA        supply.    -   (vii) Each D/A has an output 1 to a pad.    -   (viii) The D/A outputs are high impedance. Loading current must        be less than 1 nA.    -   (ix) The D/A pads can be programmed to output a digital signal        from a register. The output swing is from VSSA to VDDA.

Charger/Data Downloader Interface

The TX_EXT_OD 4280 is an open drain output whose input is the signal onthe TX_UP input pad. This will allow the TX_EXT_OD pad to be open in theUART idle condition. The TX_EXT_OD pad has a comparator monitoring itsvoltage. If the voltage is above the comparator threshold voltage for adebounce period (¼ second), the output, nBAT_CHRG_EN (4281), will golow. This comparator and other associated circuitry with this functionare on the VBAT and/or VDDBU planes.

The circuitry associated with this function must allow lows on TX_EXT_ODpad that result from normal communication with an external devicewithout disabling the assertion of nBAT_CHRG_EN. If POR1 is active,nBAT_CHRG_EN will be high (not asserted). The comparator's thresholdvoltage is between 0.50V and 1.2V. The comparator will have hysteresis;The falling threshold is approximately 25 mV lower than the risingthreshold.

The nRX_EXT pad inverts the signal on this pad and output it to RX_UP.In this way, the nRX_EXT signal will idle low. The nRX_EXT must acceptinputs up to VBAT voltage. The nRX_EXT threshold is 1.22V±3%. The outputof this comparator will be available over the SPI bus for amicroprocessor to read.

The nRX_EXT pad also incorporates a means to programmably source acurrent, which will be 80±30 nA, with the maximum voltage being VBAT.The ASIC layout has mask programmable options to adjust this currentfrom 30 nA to 200 nA in less than 50 nA steps with a minimal number ofmask layer changes. A programmable bit will be available to block theUART break detection and force the RX_UP high. In normal operation, thisbit will be set high before enabling the current sourcing to nRX_EXT andthen set low after the current sourcing is disabled to ensure that noglitches are generated on RX_UP or that a UART break event is generated.Note to implement a wet connector detector, while the current sourceinto nRX_EXT is active, an RX comparator output indicating a low inputvoltage would indicate leakage current. The ASIC includes a pulldownresistor approximately 100 k ohms on the nRX_EXT pad. This pulldown willbe disconnected when the current source is active.

Sensor Connect Switch

The ASIC shall have a pad, SEN_CONN_SW (4282), which is able to detect alow resistance to VSS (4284). The SEN_CONN_SW sources a current from 5to 25 uA with SEN_CONN_SW=0V and has a maximum open circuit voltage of0.4V. The ASIC layout has mask programmable options to adjust thiscurrent from 1 uA to 20 uA in less than 5 uA steps with a minimal numberof mask layer changes. The SEN_CONN_SW has associated circuitry thatdetects the presence of a resistance between SEN_CONN_SW and VSSA (4234)whose threshold is between 2 k and 15 k ohms. The average current drainof this circuit is 50 nA max. Sampling must be used to achieve this lowcurrent.

Oscillator Calibration Circuit

The ASIC has counters whose inputs can be steered to internal orexternal clock sources. One counter generates a programmable gatinginterval for the other counter. The gating intervals include 1 to 15seconds from the 32 kHz oscillator. The clocks that can be steered toeither counter are 32 kHz, RC oscillator, High Speed RC oscillator, andan input from any GPIO pad.

Oscillator Bypassing

The ASIC can substitute external clocks for each of the oscillators'outputs. The ASIC has a register that can be written only when aspecific TEST_MODE is asserted. This register has bits to enable theexternal input for the RC Oscillator, and may be shared with otheranalog test control signals. However, this register will not allow anyoscillator bypass bits to be active if the TEST_MODE is not active.

The ASIC also has an input pad for an external clock to bypass the RCOscillator. The pad, GPIO_VBAT, is on the VBAT power plane. The ASICfurther includes a bypass enable pad for the 32 KHZ oscillator,OSC32K_BYPASS. When high, the 32 KHZ oscillator output is supplied bydriving the OSC32 KHZ_IN pad. It is noted that, normally, the OSC32KHZ_IN pad is connected to a crystal.

The ASIC has inputs for an external clock to bypass the HS_RC_OSC. Thebypass is enabled by a programmable register bit. The HS_RC_OSC may besupplied programmably by either the GPIO on the VDD plane or by GPIOs onthe VPAD plane.

SPI Slave Port

The SPI slave port includes an interface consisting of a chip selectinput (SPI_nCS) 4289, a clock input (SPI_CK) 4286, a serial data input(SPI_MOSI) 4287, and a serial data output (SPI_MISO) 4288. The chipselect input (SPI_nCS) is an active low input, asserted by an off-chipSPI master to initiate and qualify an SPI transaction. When SPI_nCS isasserted low, the SPI slave port configures itself as a SPI slave andperforms data transactions based on the clock input (SPI_CK). WhenSPI_nCS is inactive, the SPI slave port resets itself and remains inreset mode. As this SPI interface supports block transfers, the mastershould keep SPI_nCS low until the end of a transfer.

The SPI clock input (SPI_CK) will always be asserted by the SPI master.The SPI slave port latches the incoming data on the SPI_MOSI input usingthe rising edge of SPI_CK and driving the outgoing data on the SPI_MISOoutput using the falling edge of SPI_CK. The serial data input(SPI_MOSI) is used to transfer data from the SPI master to the SPIslave. All data bits are asserted following the falling edge of SPI_CK.The serial data output (SPI_MISO) is used to transfer data from the SPIslave to the SPI master. All data bits are asserted following thefalling edge of SPI_CK.

SPI_nCS, SPI_CK and SPI_MOSI are always driven by the SPI master, unlessthe SPI master is powered down. If VPAD_EN is low, these inputs areconditioned so that the current drain associated with these inputs isless than 10 nA and the SPI circuitry is held reset or inactive.SPI_MISO is only driven by the SPI slave port when SPI_nCS is active,otherwise, SPI_MISO is tri-stated.

The chip select (SPI_nCS) defines and frames the data transfer packet ofan SPI data transaction. The data transfer packet consists of threeparts. There is a 4-bit command section followed by a 12-bit addresssection, which is then followed by any number of 8 bit data bytes. Thecommand bit 3 is used as the direction bit. A “1” indicates a writeoperation, and a “0” indicates a read operation. The combinations ofcommand bit 2, 1 and 0 have the following definitions. Unusedcombinations are undefined.

-   -   (i) 0000: read data and increment address.    -   (ii) 0001: read data, no change to address    -   (iii) 0010: read data, decrement address    -   (iv) 1000: write data and increment address    -   (v) 1001: write data, no change to address    -   (vi) 1010: write data, decrement address    -   (vii) x011: Test Port Addressing

The 12-bit address section defines the starting byte address. If SPI_nCSstays active after the first data byte, to indicate a multi-bytetransfer, the address is incremented by one after each byte istransferred. Bit<11> of the address (of address<11:0>) indicates thehighest address bit. The address wraps around after reaching theboundary.

Data is in the byte format, and a block transfer can be performed byextending SPI_nCS to allow all bytes to be transferred in one packet.

Microprocessor Interrupt

The ASIC has an output at the VPAD logic level, UP_INT, for the purposeof sending interrupts to a host microprocessor. The microprocessorinterrupt module consists of an interrupt status register, an interruptmask register, and a function to logically OR all interrupt statusesinto one microprocessor interrupt. The interrupt is implemented tosupport both edge sensitive and level sensitive styles. The polarity ofthe interrupt is programmable. The default interrupt polarity is TBD.

In a preferred embodiment, all interrupt sources on the AFE ASIC will berecorded in the interrupt status register. Writing a “1” to thecorresponding interrupt status bit clears the corresponding pendinginterrupt. All interrupt sources on the AFE ASIC are mask-able throughthe interrupt mask register. Writing a “1” to the correspondinginterrupt mask bit enables the masking of the corresponding pendinginterrupt. Writing a “0” to the corresponding interrupt mask bitdisables the masking of the corresponding interrupt. The default stateof the interrupt mask register is TBD.

General Purpose Input/Outputs (GPIOs)/Parallel Test Port

In embodiments, the ASIC may have eight GPIOs that operate on VPAD levelsignals. The ASIC has one GPIO that operates on a VBAT level signal, andone GPIO that operates on a VDD level signal. All of the GPIOs have atleast the following characteristics:

-   -   (i) Register bits control the selection and direction of each        GPIO.    -   (ii) The ASIC has a means to configure the GPIOs as inputs that        can be read over the SPI interface.    -   (iii) The ASIC has a means to configure the GPIOs as input to        generate an interrupt.    -   (iv) The ASIC has a means to configure each GPIO as an output to        be controlled by a register bit that can be written over the SPI        interface.    -   (v) Programmably, the ASIC is able to output an input signal        applied to GPIO_VBAT or GPIO_VDD to a GPIO (on the VPAD power        plane). (Level shifting function).    -   (vi) The ASIC has a means to configure each GPIO as an input to        the oscillator calibration circuit.    -   (vii) The ASIC has a means to configure each general purpose        comparator output to at least one GPIO on each power plane. The        polarity of the comparator output is programmable by a        programmable bit.    -   (viii) The GPIOs have microprocessor interrupt generating        capability.    -   (ix) The GPIOs are programmable to open drain outputs.    -   (x) The GPIOs on the VPAD power plane are configurable to        implement boot control of a microprocessor.

A Parallel Test Port shares the 8-bit GPIOs on the VPAD voltage plane.The test port will be used for observing register contents and variousinternal signals. The outputs of this port are controlled by the portconfiguration register in the normal mode. Writing 8′hFF to bothGPIO_O1S_REG & GPIO_O2S_REG registers will steer the test port data onthe GPIO outputs, while writing 8′h00 to the GPIO_ON_REG register willdisable the test port data and enable the GPIO data onto the GPIOoutputs.

Registers and pre-grouped internal signals can be observed over thistest port by addressing the target register through the SPI slave port.The SPI packet has the command bits set to 4′b0011 followed by the12-bit target register address. The parallel test port continues todisplay the content of the addressed register until the next Test PortAddressing command is received.

Analog Test Ports

The IC has a multiplexer feeding the pad, TP_ANAMUX (4290), which willgive visibility to internal analog circuit nodes for testing. The ICalso has a multiplexer feeding the pad, TP_RES (4260), which will givevisibility to internal analog circuit nodes for testing. This pad willalso accommodate a precision 1 meg resistor in usual application toperform various system calibrations.

Chip ID

The ASIC includes a 32 bit mask programmable ID. A microprocessor usingthe SPI interface will be able to read this ID. This ID is to be placedin the analog electronics block so that changing the ID does not requirea chip reroute. The design should be such that only one metal or onecontact mask change is required to change the ID.

Spare Test Outputs

The ASIC has 16 spare digital output signals that can be multiplexed tothe 8 bit GPIO under commands sent over the SPI interface. These signalswill be organized as two 8 bit bytes, and will be connected to VSS ifnot used.

Digital Testing

The ASIC has a test mode controller that uses two input pins, TEST_CTL0(4291) and TEST_CTL1 (4292). The test controller generates signals fromthe combination of the test control signals that have the followingfunctionality (TEST_CTL<1:0>):

-   -   (i) 0 is normal operating mode;    -   (ii) 1 is Analog Test Mode;    -   (iii) 2 is Scan Mode;    -   (iv) 3 is Analog Test mode with the VDD_EN controlled by an        input to GPIO_VBAT.

The test controller logic is split between the VDD and VDDBU powerplanes. During scan mode, testing LT_VBAT should be asserted high tocondition the analog outputs to the digital logic. The ASIC has a scanchain implemented in as much digital logic as reasonably possible forfast digital testing.

Leakage Test Pin

The ASIC has a pin called LT_VBAT that, when high, will put all theanalog blocks into an inactive mode so that only leakage currents willbe drawn from the supplies. LT_VBAT causes all digital outputs fromanalog blocks to be in a stable high or low state as to not affectinterface logic current drain. The LT_VBAT pad is on the VBAT plane witha pulldown with a resistance between 10 k and 40 k ohms.

Power Requirements

In embodiments of the inventions herein, the ASIC includes a low powermode where, at a minimum, the microprocessor clock is off, the 32 kHzreal time clock runs, and circuitry is active to detect a sensorconnection, a change of level of the WAKE_UP pin, or a BREAK on thenRX_EXT input. This mode has a total current drain from VBAT (VDDBU),VDD, and VDDA of 4.0 uA maximum. When the Battery Protection Circuitdetects a low battery (see Battery Protection Circuit description), theASIC goes to a mode with only the VBAT and VDDBU power planes active.This is called Low Battery state. The VBAT current in this mode is lessthan 0.3 uA.

With the ASIC programmed to the potentiostat configuration with any oneWORK electrode active in the H2O2 (peroxide) mode with its voltage setto 1.535V, the COUNTER amplifier on with the VSET_RE set to 1.00V, a 20MEG load resistor connected between WORK and the COUNTER, the COUNTERand RE connected together and assuming one WORK electrode currentmeasurement per minute, the average current drain of all power suppliesis less than 7 uA. The measured current after calibration should be26.75 nA±3%. Enabling additional WORK electrodes increases the combinedcurrent drain by less than 2 uA with the WORK electrode current of 25nA.

With the ASIC programmed to the potentiostat configuration with thediagnostic function enabled to measure the impedance of one of the WORKelectrodes with respect to the COUNTER electrode, the ASIC is configuredto meet the following:

-   -   (i) Test frequencies: 0.1, 0.2, 0.3, 0.5 Hz, 1.0, 2.0, 5.0, 10,        100, 1000 and 4000 Hz.    -   (ii) The measurement of the above frequencies is not to exceed        50 seconds.    -   (iii) The total charge supplied to the ASIC is less than 8        millicoulombs.

Environment

In preferred embodiments of the invention, the ASIC:

-   -   (i) Operates and meets all specifications in the commercial        temperature range of 0 to 70° C.    -   (ii) Functionally operates between −20° C. and 80° C., but may        do so with reduced accuracy.    -   (iii) Is expected to operate after being stored in a temperature        range of −30 to 80° C.    -   (iv) Is expected to operate in the relative humidity range of 1%        to 95%.    -   (v) ESD protection is greater than ±2 KV, Human Body Model on        all pins when packaged in a TBD package, unless otherwise        specified.    -   (vi) Is configured such that the WORK1-WORK5, COUNTER, RE,        TX_EXT_OD, and nRX_EXT pads withstand greater than ±4 KV Human        Body Model.    -   (vii) Is configured such that the leakage current of the        WORK1-WORK5 and RE pads is less than 0.05 nA at 40° C.

In embodiments of the invention, the ASIC may be fabricated in 0.25micron CMOS process, and backup data for the ASIC is on DVD disk,916-TBD.

As described in detail hereinabove, the ASIC provides the necessaryanalog electronics to provide the following, among others: (i) supportmultiple potentiostats and interface with multi-terminal glucose sensorsbased on either Oxygen or Peroxide; (ii) interface with amicrocontroller so as to form a micropower sensor system; and (iii)implement EIS diagnostics based on measurement of EIS-based parameters.The measurement and calculation of EIS-based parameters will now bedescribed in accordance with embodiments of the inventions herein.

As has been mentioned previously, the impedance at frequencies in therange from 0.1 Hz to 8 kHz can provide information as to the state ofthe sensor electrodes. The AFE IC circuitry incorporates circuitry togenerate the measurement forcing signals and circuitry to makemeasurements used to calculate the impedances. The design considerationsfor this circuitry include current drain, accuracy, speed ofmeasurement, the amount of processing required, and the amount of ontime required by a control microprocessor.

In a preferred embodiment of the invention, the technique the AFE ICuses to measure the impedance of an electrode is to superimpose a sinewave voltage on the dc voltage driving an electrode and to measure thephase and amplitude of the resultant AC current. To generate the sinewave, the AFE IC incorporates a digitally-synthesized sine wave current.This digital technique is used because the frequency and phase can beprecisely controlled by a crystal derived timebase and it can easilygenerate frequencies from DC up to 8 kHz. The sine wave current isimpressed across a resistor in series with a voltage source in order toadd the AC component to the electrode voltage. This voltage is the ACforcing voltage. It is then buffered by an amplifier that drives aselected sensor electrode.

The current driving the electrode contains the resultant AC currentcomponent from the forcing sine wave and is converted to a voltage. Thisvoltage is then processed by multiplying it by a square wave that has afixed phase relative to the synthesized sine wave. This multipliedvoltage is then integrated. After the end of a programmable number ofintegration intervals—an interval being an integral number of ½ periodsof the driving sine wave—the voltage is measured by the ADC. Bycalculations involving the values of the integrated voltages, the realand imaginary parts of the impedance can be obtained.

The advantage of using integrators for the impedance measurement is thatthe noise bandwidth of the measurement is reduced significantly withrespect to merely sampling the waveforms. Also, the sampling timerequirements are significantly reduced which relaxes the speedrequirement of the ADC.

FIG. 45 shows the main blocks of the EIS circuitry in the AFE IC(designated by reference numeral 4255 in FIG. 42B). The IDAC 4510generates a stepwise sine wave in synchrony with a system clock. A highfrequency of this system clock steps the IDAC through the lookup tablethat contains digital code. This code drives the IDAC, which generatesan output current approximating a sine wave. This sine wave current isforced across a resistor to give the AC component, Vin_ac, with the DCoffset, VSET8 (4520). When the IDAC circuit is disabled, the DC outputvoltage reverts to VSET8, so the disturbance to the electrodeequilibrium is minimized. This voltage is then buffered by an amplifier4530 that drives the electrode through a resistor in series, Rsense. Thedifferential voltage across Rsense is proportional to the current. Thisvoltage is presented to a multiplier 4540 that multiplies the voltage byeither +1 or −1. This is done with switches and a differential amplifier(instrumentation amplifier). The system clock is divided to generate thephase clock 4550 which controls the multiply function and can be set to0, 90, 180 or 270 degrees relative to the sine wave.

The plots in FIGS. 46A-46F and 47A-47F show a simulation of the signalsof the circuit shown in FIG. 45 to a current that has 0 degree phaseshift, which represents a real resistance. For these examplesimulations, the simulation input values were selected to give thecurrent sense voltage equal to 0.150V. To obtain enough information toderive the impedance and phase, two integrations are required: one witha 0 degree phase multiply (FIGS. 46A-46F) and one with a 90 degree phasemultiply (FIGS. 47A-47F).

Calculation of Impedance

The equations describing the integrator output are provided below. Forsimplicity, only ½ of a sine wave period is considered. As can be seenfrom the plots of FIGS. 46A-46F and 47A-47F, total integrator outputwill be approximately the integrated value of a ½ sine wave cyclemultiplied by the number of ½ cycles integrated. It is noted that themultiplying switches in relation with the integrate time perform a“gating” function of the signal to the integrator; this can be viewed assetting the limits of integration. The multiplying signal has a fixedphase to the generated sine wave. This can be set to 0, 90, 180, or 270degrees with software. If the sine wave is in phase (0 degree shift)with respect to the multiply square wave, the limits of integration willbe π (180°) and 0 (0°). If the sine wave is shifted by 90 degrees, thelimits of integration can be viewed as ¾π (270°) and ¼π (900).

The formulas with the multiplying square wave in-phase (0°) with respectto the driving sine wave are shown below. This will yield a voltage thatis proportional to the real component of the current. It is noted that Φis the phase shift of the sine wave relative to the multiplying squarewave; Vout is the integrator output, and Aampl is the current sine waveamplitude. Also the period of the sine wave is 1/f, and RC is the timeconstant of the integrator.

$v_{{out}\mspace{11mu} 0} = {{\int_{0}^{\frac{1}{2f}}{\frac{V_{in}}{RC}\ {\partial t}}} = {{\frac{A_{ampl}}{RC}{\int_{0}^{\frac{1}{2f}}{\sin \left\lbrack {{2\pi \; f{\partial t}} + \varphi} \right\rbrack}}} = {{{{- \frac{A_{ampl}}{2\pi \; {fRC}}}{\cos \left\lbrack {{2\pi \; {ft}} + \varphi} \right\rbrack}}\ |_{0}^{\frac{1}{2f}}\mspace{20mu} v_{{out}\; 0}} = {- {\frac{A_{ampl}}{2\pi \; f\; {RC}}\left\lbrack {{\cos \left\lbrack {\pi + \varphi} \right\rbrack} - {\cos \lbrack\varphi\rbrack}} \right\rbrack}}}}}$  cos (φ + ϕ) = cos (φ)cos (ϕ) − sin (φ)sin (ϕ);  cos (π + φ) = −cos (φ);   cos (−φ) = cos (φ)$v_{{out}\mspace{11mu} 0} = {{\frac{- A_{ampl}}{2\pi \; {fRC}}\left\lbrack {{\cos \left( {\pi + \varphi} \right)} - {\cos (\varphi)}} \right\rbrack} = {{\frac{A_{ampl}}{2\pi \; {fRC}}\left\lbrack {{\cos (\varphi)} + {\cos (\varphi)}} \right\rbrack} = {\frac{A_{ampl}}{\pi \; {fRC}}{\cos (\varphi)}}}}$

If Φ=0,

$v_{{out}\; 0} = {\frac{A_{ampl}}{\pi \; f\; {RC}}.}$

This corresponds to the real part of the current.

For the multiplying square wave quadrature phase (90°) with respect tothe driving sine wave to yield an output proportional to the imaginarycomponent of the current:

$v_{{out}\mspace{11mu} 90} = {{\int_{\frac{1}{4f}}^{\frac{3}{4f}}{\frac{V_{in}}{RC}\ {\partial t}}} = {{\frac{A_{ampl}}{RC}{\int_{\frac{1}{4f}}^{\frac{3}{4f}}{\sin \left\lbrack {{2\pi \; f{\partial t}} + \varphi} \right\rbrack}}} = {\left. {{- \frac{A_{ampl}}{2\pi \; {fRC}}}{\cos \left\lbrack {{2\pi \; {ft}} + \varphi} \right\rbrack}}\  \middle| {}_{\frac{\frac{3}{4f}}{\frac{1}{4f}}}\mspace{20mu} v_{{out}\mspace{11mu} 90} \right. = {- {\frac{A_{ampl}}{2\pi \; f\; {RC}}\left\lbrack {{\cos \left\lbrack {{\frac{3}{2}\pi} + \varphi} \right\rbrack} - {\cos \left\lbrack {{\frac{1}{2}\pi} + \varphi} \right\rbrack}} \right\rbrack}}}}}$  cos (φ + ϕ) = cos (φ)cos (ϕ) − sin (φ)sin (ϕ);$\mspace{20mu} {{{\cos \left\lbrack {{\frac{3}{2}\pi} + \varphi} \right\rbrack} = {\sin (\varphi)}};}$$\mspace{20mu} {{\cos \left\lbrack {{\frac{1}{2}\pi} + \varphi} \right\rbrack} = {- {\sin (\varphi)}}}$$v_{{out}\mspace{11mu} 90} = {{\frac{- A_{ampl}}{2\pi \; {fRC}}\left\lbrack {{\sin (\varphi)} + {\sin (\varphi)}} \right\rbrack} = {{\frac{- A_{ampl}}{2\pi \; {fRC}}\left\lbrack {{\sin (\varphi)} + {\sin (\varphi)}} \right\rbrack} = {\frac{- A_{ampl}}{\pi \; {fRC}}{\sin (\varphi)}}}}$

If Φ=0,

$v_{{out}\mspace{11mu} 90} = {{\frac{A_{ampl}}{\pi \; f\; {RC}}{\sin (\varphi)}} = 0.}$

This corresponds to the imaginary part of the current.

In the first example plot shown in FIGS. 46A-46F, A_(ampl) is 0.150v,the frequency is 1 kHz, Φ=0, the RC for the integrator is 20M ohm and 25pF which gives RC=0.5 msec. Plugging in those numbers into theequations, gives 0.09549v, which favorably compares to the integratoroutput of the plot in FIG. 46. It is noted that the integrator outputover the period of integration is the delta voltage from the start ofintegration to the measurement.

For the 90° square wave multiply, the result should be 0 since sin(0)=0.The simulation result is close to this value.

To Calculate the Phase:

since

${\frac{v_{{out}\; 90}}{v_{{out}\; 0}} = \frac{\sin (\varphi)}{\cos (\varphi)}},$

it follows:

$\varphi = {{\arctan \frac{\sin (\varphi)}{\cos (\varphi)}} = {\arctan \frac{v_{{out}\; 90}}{v_{{out}\; 0}}}}$

where V_(out90) is the integrator output with the 90° phase shift forthe multiply, and V_(out0) is the integrator output for the 0° phaseshift. The V_(out90) and V_(out0) outputs must be integrated for thesame number of ½ cycles or normalized by the number of cycles. It isimportant to note that, in the actual software (e.g., ASIC)implementation, only integral cycles (360°) are allowed because anintegral number of cycles compensates for any offset in the circuitrybefore the multiplier.

The magnitude of the current can be found from

${I} = {{\frac{A_{ampl}}{R_{sense}}\mspace{14mu} {and}\mspace{14mu} A_{ampl}} = {\frac{v_{{out\_}90}\pi \; {fRC}}{\sin (\varphi)}{\mspace{11mu} \;}{or}}}$${A_{ampl} = \frac{v_{{out\_}0}\pi \; {fRC}}{\cos (\varphi)}},$

or A_(ampl)==πfRC√{square root over (V_(out) _(_) ₀ ^(2+V) _(out) _(_)₉₀ ²)}. This current has the phase angle as calculated above.

The above analysis shows that one can determine the current amplitudeand its phase with respect to the multiplying signal. The forcingvoltage is generated in a fixed phase (0, 90, 180 or 270 degrees) withrespect to the multiplying signal—this is done digitally so that it isprecisely controlled. But there is at least one amplifier in the pathbefore the forcing sine wave is applied to the electrode; this willintroduce unwanted phase shift and amplitude error. This can becompensated for by integrating the forcing sine wave signal obtainedelectrically near the electrode. Thus, the amplitude and any phase shiftof the forcing voltage can be determined. Since the path for both thecurrent and voltage waveform will be processed by the same circuit, anyanalog circuit gain and phase errors will cancel.

Since the variable of interest is the impedance, it may not be necessaryto actually calculate the A_(ampl). Because the current waveform and thevoltage waveform are integrated through the same path, there exists asimple relationship between the ratio of the current and the voltage.Calling the integrated current sense voltage V_(I) _(_) _(out) and theintegrated electrode voltage as V_(V) _(_) _(out) with the additionalsubscript to describe the phase of the multiplying function:

${I = {{\frac{A_{I\_ ampl}}{R_{sense}}{\angle\varphi}} = {\frac{V_{{I\_ out}\_ 0}\pi \; {fRC}}{{\cos (\varphi)}R_{sense}}{\angle\varphi}}}};$$V = {{A_{V\_ ampl}{\angle\theta}} = {\frac{V_{{V\_ out}\_ 0}\pi \; {fRC}}{\cos (\theta)}{\angle\theta}}}$

The impedance will be the voltage divided by the current. Thus,

$Z = {\frac{{V}{\angle\theta}}{{I}{\angle\varphi}} = {\frac{\frac{V_{{V\_ out}\_ 0}\pi \; {fRC}\; \angle \; \theta}{\cos (\theta)}}{\frac{V_{{I\_ out}\_ 0}\pi \; {fRC}\; \angle \; \varphi}{{\cos (\theta)}R_{sense}}} = {R_{sense}*\frac{V_{{V\_ out}\_ 0}{\cos (\varphi)}}{V_{{I\_ out}\_ 0}{\cos (\theta)}}{\angle \left( {\theta - \varphi} \right)}}}}$

The magnitudes of the voltage and the current can also be obtained fromthe square root of the squares of the 0 and 90 degree phase integrationvoltages. As such, the following may also be used:

$\begin{matrix}{Z = \frac{{V}{\angle\theta}}{{I}{\angle\varphi}}} \\{= \frac{\sqrt{V_{{V\_ out}\_ 0}^{2} + V_{{V\_ out}\_ 90}^{2}}{\angle\theta}}{\sqrt{V_{{I\_ out}\_ 0}^{2} + V_{{I\_ out}\_ 90}^{2}}{\angle\varphi}}} \\{= {R_{sense}*\frac{\sqrt{V_{{V\_ out}\_ 0}^{2} + V_{{V\_ out}\_ 90}^{2}}}{\sqrt{V_{{I\_ out}\_ 0}^{2} + V_{{I\_ out}\_ 90}^{2}}}{\angle \left( {\theta - \varphi} \right)}}}\end{matrix}$

The integration of the waveforms may be done with one hardwareintegrator for the relatively-higher frequencies, e.g., those aboveabout 256 Hz. The high frequencies require four measurement cycles: (i)one for the in-phase sensor current; (ii) one for the 90 degree out ofphase sensor current; (iii) one for the in-phase forcing voltage; and(iv) one for the 90 degree out of phase forcing voltage.

Two integrators may be used for the relatively-lower frequencies, e.g.,those lower than about 256 Hz, with the integration value consisting ofcombining integrator results numerically in the system microprocessor.Knowing how many integrations there are per cycle allows themicroprocessor to calculate the 0 and 90 degree componentsappropriately.

Synchronizing the integrations with the forcing AC waveform and breakingthe integration into at least four parts at the lower frequencies willeliminate the need for the hardware multiplier as the combining of theintegrated parts in the microprocessor can accomplish the multiplyingfunction. Thus, only one integration pass is necessary for obtaining thereal and imaginary current information. For the lower frequencies, theamplifier phase errors will become smaller, so below a frequency, e.g.,between 1 Hz and 50 Hz, and preferably below about 1 Hz, the forcingvoltage phase will not need to be determined. Also, the amplitude couldbe assumed to be constant for the lower frequencies, such that only onemeasurement cycle after stabilization may be necessary to determine theimpedance.

As noted above, whereas one hardware integrator is used for therelatively-higher frequencies, for the relatively-lower frequencies, twointegrators may be used. In this regard, the schematic in FIG. 45 showsthe EIS circuitry in the AFE IC as used for the relatively-higher EISfrequencies. At these frequencies, the integrator does not saturatewhile integrating over a cycle. In fact, multiple cycles are integratedfor the highest frequencies as this will provide a larger output signalwhich results in a larger signal to noise ratio.

For the relatively-lower frequencies, such as, e.g., those below about500 Hz, the integrator output can saturate with common parameters.Therefore, for these frequencies, two integrators are used that arealternately switched. That is, while a first integrator is integrating,the second integrator is being read by the ADC and then is reset(zeroed) to make it ready to integrate when the integration time forfirst integrator is over. In this way, the signal can be integratedwithout having gaps in the integration. This would add a secondintegrator and associated timing controls to the EIS circuitry shown inFIG. 45.

Stabilization Cycle Considerations

The above analysis is for steady state conditions in which the currentwaveform does not vary from cycle to cycle. This condition is not metimmediately upon application of a sine wave to a resistor-capacitor (RC)network because of the initial state of the capacitor. The current phasestarts out at 0 degrees and progresses to the steady state value.However, it would be desirable for the measurement to consume a minimumamount of time in order to reduce current drain and also to allowadequate time to make DC sensor measurements (Isigs). Thus, there is aneed to determine the number of cycles necessary to obtain sufficientlyaccurate measurements.

The equation for a simple RC circuit—with a resistor and capacitor inseries—is

${v_{ac} = {{R*{I(t)}} + {\frac{1}{C}{\int{{I(t)}{\partial t}}}}}}\ $

Solving the above for I(t) gives:

${I(t)} = {{{\frac{- 1}{RC}\left\lbrack {{V_{c\; 0}C} + \frac{\omega \; V_{m}}{R\left\lbrack {\omega^{2} + \frac{1}{R^{2}C^{2}}} \right\rbrack}} \right\rbrack}e^{\frac{- t}{RC}}} + {{\frac{V_{m}}{R}\left\lbrack \frac{1}{\left\lbrack {\omega^{2} + \frac{1}{R^{2}C^{2}}} \right\rbrack} \right\rbrack}\left\lbrack {{\omega^{2}{\sin \left( {\omega \; t} \right)}} + {\frac{\omega}{RC}\; \cos \; \omega \; t}} \right\rbrack}}$

where V_(c0) is the initial value of the capacitor voltage, V_(m) is themagnitude of the driving sine wave, and ω is the radian frequency (2πf).

The first term contains the terms defining the non-steady statecondition. One way to speed the settling of the system would be to havethe first term equal 0, which may be done, e.g., by setting

${V_{cinit}C} = {{\frac{\omega \; V_{m}}{R\left\lbrack {\omega^{2} + \frac{1}{R^{2}C^{2}}} \right\rbrack}\mspace{14mu} {or}\mspace{14mu} V_{cinit}} = \frac{{RC}\; \omega \; V_{m}}{\left\lbrack {{R^{2}C^{2}\omega^{2}} + 1} \right\rbrack}}$

While this may not be necessary in practice, it is possible to set theinitial phase of the forcing sine wave to jump immediately from the DCsteady state point to V_(cinit). This technique may be evaluated for thespecific frequency and anticipated phase angle to find the possiblereduction in time.

The non-steady state term is multiplied by the exponential function oftime. This will determine how quickly the steady state condition isreached. The RC value can be determined as a first order approximationfrom the impedance calculation information. Given the following:

${X_{c} = {\frac{1}{\omega \; C} = {{z\mspace{14mu} \sin \mspace{14mu} \varphi \mspace{14mu} {and}\mspace{14mu} R} = {Z\mspace{14mu} \cos \mspace{14mu} \varphi}}}},{{{it}\mspace{14mu} {follows}\mspace{14mu} {that}\mspace{14mu} {RC}} = {\frac{Z\mspace{14mu} \cos \mspace{14mu} \varphi}{\omega \; Z\mspace{14mu} \sin \mspace{14mu} \varphi} = \frac{1}{\omega \mspace{14mu} \tan \mspace{14mu} \varphi}}}$

For a sensor at 100 Hz with a 5 degree phase angle, this would mean atime constant of 18.2 msec. For settling to less than 1%, this wouldmean approximately 85 msec settling time or 8.5 cycles. On the otherhand, for a sensor at 0.10 Hz with a 65 degree phase angle, this wouldmean a time constant of 0.75 sec. For settling to less than 1%, thiswould mean approximately 3.4 sec settling time.

Thus, in embodiments of the inventions as detailed hereinabove, the ASICincludes (at least) 7 electrode pads, 5 of which are assigned as WORKelectrodes (i.e., sensing electrodes, or working electrodes, or WEs),one of which is labeled COUNTER (i.e., counter electrode, or CE), andone that is labeled REFERENCE (i.e., reference electrode, or RE). Thecounter amplifier 4321 (see FIG. 42B) may be programmably connected tothe COUNTER, the REFERENCE, and/or any of the WORK assigned pads, and inany combination thereof. As has been mentioned, embodiments of theinventions herein may include, e.g., more than five WEs. In this regard,embodiments of the inventions herein may also be directed to an ASICthat interfaces with more than 5 working electrodes.

It is important to note that, with the ASIC as described herein, each ofthe above-mentioned five working electrodes, the counter electrode, andthe reference electrode is individually and independently addressable.As such, any one of the 5 working electrodes may be turned on andmeasure Isig (electrode current), and any one may be turned off.Moreover, any one of the 5 working electrodes may be operablyconnected/coupled to the EIS circuitry for measurement of EIS-relatedparameters, e.g., impedance and phase. In other words, EIS may beselectively run on any one or more of the working electrodes. Inaddition, the respective voltage level of each of the 5 workingelectrodes may be independently programmed in amplitude and sign withrespect to the reference electrode. This has many applications, such as,e.g., changing the voltage on one or more electrodes in order to makethe electrode(s) less sensitive to interference.

In embodiments where two or more working electrodes are employed asredundant electrodes, the EIS techniques described herein may be used,e.g., to determine which of the multiplicity of redundant electrodes isfunctioning optimally (e.g., in terms of faster start-up, minimal or nodips, minimal or no sensitivity loss, etc.), so that only the optimalworking electrode(s) can be addressed for obtaining glucosemeasurements. The latter, in turn, may drastically reduce, if noteliminate, the need for continual calibrations. At the same time, theother (redundant) working electrode(s) may be: (i) turned off, whichwould facilitate power management, as EIS may not be run for the “off”electrodes; (ii) powered down; and/or (iii) periodically monitored viaEIS to determine whether they have recovered, such that they may bebrought back on line. On the other hand, the non-optimal electrode(s)may trigger a request for calibration. The ASIC is also capable ofmaking any of the electrodes—including, e.g., a failed or off-lineworking electrode—the counter electrode. Thus, in embodiments of theinventions herein, the ASIC may have more than one counter electrode.

While the above generally addresses simple redundancy, wherein theredundant electrodes are of the same size, have the same chemistry, thesame design, etc., the above-described diagnostic algorithms, fusionmethodologies, and the associated ASIC may also be used in conjunctionwith spatially distributed, similarly sized or dissimilarly sized,working electrodes as a way of assessing sensor implant integrity as afunction of implant time. Thus, in embodiments of the inventions herein,sensors may be used that contain electrodes on the same flex that mayhave different shapes, sizes, and/or configurations, or contain the sameor different chemistries, used, e.g., to target specific environments.

In embodiments of the inventions herein, a sensor system employingcomplex redundancy includes two (or more) sensors, of which (at least)two sensors are dissimilar to one another in design (and may also employdifferent chemistry and/or size). Here, one (or more) of the sensors maybe designed to have, e.g., considerably better hydration and/orstabilization characteristics, but may not last past 2 or 3 days. Theother sensor(s), on the other hand, may have long-lasting durability,but slow initial hydration and/or stabilization. In such a case, analgorithm may be designed whereby the first sensor(s) is used togenerate glucose data during early wear, after which, during mid-wear,the first sensor(s) may be used to calibrate the second sensor(s), andthen a switch-over may be made (e.g., via the ASIC) to the secondsensor(s) for generating glucose data during the remainder of the lifeof the glucose sensor system. As will be described in more detailhereinbelow, in such a system, the fusion algorithm(s) described hereinmay be used—in conjunction with the ASIC described herein—to provide forthe switchover, as well as fusion of data from two or more of theworking electrodes that are employed in the sensors, with theuser/patient remaining unaware that data was fused, or that aswitched-over was implemented between sensors during mid-wear. In someembodiments, signals may not necessarily be fused to generate a sensorglucose (SG) output, as different working electrodes may be tapped atdifferent times.

In yet other embodiments, the overall sensor design may include workingelectrodes (WEs) of different sizes. Such smaller WEs generally output alower Isig (smaller geometric area) and may be used specifically forhypoglycemia detection/accuracy, while larger WEs—which output a largerIsig—may be used specifically for euglycemia and hyperglycemia accuracy.Given the size differences, different EIS thresholds and/or frequenciesmust be used for diagnostics as among these electrodes. The ASIC, asdescribed hereinabove, accommodates such requirements by enablingprogrammable, electrode-specific, EIS criteria. As with some of theprevious examples, here, signals may not necessarily be fused togenerate an SG output (i.e., different WEs may be tapped at differenttimes).

As was noted previously, the ASIC includes a programmable sequencer 4266that commands the start and stop of the stimulus and coordinates themeasurements of the EIS-based parameters for frequencies above about 100Hz. At the end of the sequence, the data is in a buffer memory, and isavailable for a microprocessor to quickly obtain (values of) the neededparameters. This saves time, and also reduces system power requirementsby requiring less microprocessor intervention.

For frequencies lower than about 100 Hz, the programmable sequencer 4266coordinates the starting and stopping of the stimulus for EIS, andbuffers data. Either upon the end of the measurement cycle, or if thebuffer becomes close to full, the ASIC may interrupt the microprocessorto indicate that it needs to gather the available data. The depth of thebuffer will determine how long the microprocessor can do other tasks, orsleep, as the EIS-based parameters are being gathered. For example, inone preferred embodiment, the buffer is 64 measurements deep. Again,this saves energy as the microprocessor will not need to gather the datapiecemeal. It is also noted that the sequencer 4266 also has thecapability of starting the stimulus at a phase different from 0, whichhas the potential of settling faster.

The ASIC, as described above, can control the power to a microprocessor.Thus, for example, it can turn off the power completely, and power upthe microprocessor, based on detection of sensorconnection/disconnection using, e.g., a mechanical switch, or capacitiveor resistive sensing. Moreover, the ASIC can control the wakeup of amicroprocessor. For example, the microprocessor can put itself into alow-power mode. The ASIC can then send a signal to the microprocessorif, e.g., a sensor connect/disconnect detection is made by the ASIC,which signal wakes up the processor. This includes responding to signalsgenerated by the ASIC using techniques such as, e.g., a mechanicalswitch or a capacitive-based sensing scheme. This allows themicroprocessor to sleep for long periods of time, thereby significantlyreducing power drain.

It is important to reiterate that, with the ASIC as describedhereinabove, both oxygen sensing and peroxide sensing can be performedsimultaneously, because the five (or more) working electrodes are allindependent, and independently addressable, and, as such, can beconfigured in any way desired. In addition, the ASIC allows multiplethresholds for multiple markers, such that EIS can be triggered byvarious factors—e.g., level of V_(cntr), capacitance change, signalnoise, large change in Isig, drift detection, etc.—each having its ownthreshold(s). In addition, for each such factor, the ASIC enablesmultiple levels of thresholds.

In accordance with embodiments of the inventions herein, an equivalentcircuit model as shown in FIG. 48 may be used to model the measured EISbetween the working and reference electrodes, WE and RE, respectively.The circuit shown in FIG. 48 has a total of six (6) elements, which maybe divided into three general categories: (i) reaction-related elements;(ii) Membrane-related elements; and (iii) solution-related elements. Inthe latter category, Rsol is the solution resistance, and corresponds tothe properties of the environment external to the sensor system (e.g.,interstitial fluid in vivo).

The reaction-related elements include R_(p), which is the polarizationresistance (i.e., resistance to voltage bias and charge transfer betweenthe electrode and electrolyte), and Cdl, which is the double layercapacitance at the electrode-electrolyte interface. It is noted that,while, in this model, the double layer capacitance is shown as aconstant phase element (CPE) due to inhomogeneity of the interface, itcan also be modeled as a pure capacitance. As a CPE, the double layercapacitance has two parameters: Cdl, which denotes the admittance, andα, which denotes the constant phase of the CPE (i.e., how leaky thecapacitor is). The frequency-dependent impedance of the CPE may becalculated as

$Z_{CPE} = {\frac{1}{{{cdl}\left( {j\; \omega} \right)}^{\alpha}}.}$

Thus, the model includes two (2) reaction-related elements—R_(p) andCdl—which are represented by a total of three (3) parameters: R_(p),Cdl, and α.

The membrane-related elements include Rmem, which is the membraneresistance (or resistance due to the chemistry layer), and Cmem, whichis the membrane capacitance (or capacitance due to the chemistry layer).Although Cmem is shown in FIG. 48 as a pure capacitance, it can also bemodeled as a CPE in special cases. As shown, W is the bounded Warburgelement, and has two parameters: Y₀, which denotes the admittance of theWarburg element due to glucose/H₂O₂ diffusion within the chemistrylayer, and λ, which denotes the diffusion time constant of the Warburgelement. It is noted that Warburg may also be modeled in other ways(e.g., unbounded). The frequency-dependent impedance of the boundedWarburg element may be calculated as

$Z_{W} = {\frac{1}{Y_{0}\sqrt{j\; \omega}} \times {\coth \left( {\lambda \sqrt{j\; \omega}} \right)}}$

Thus, the model includes three (3) membrane-related elements—Rmem, Cmem,and W—which are represented by a total of four (4) parameters: Rmem,Cmem, Y₀, and λ.

The top portion of FIG. 48 shows the overall structure of a sensor inaccordance with embodiments of the invention, where Platinum Blackrefers to the electrode. Here, it is important to note that, while asingle electrode is depicted, this is by way of illustration only, andnot limitation, as the model may be applied to sensors having a greaternumber of layers, and a larger number of electrodes, than theillustrative 3-layer, single-electrode structure shown in FIG. 48. Asdescribed previously herein, GLM is the sensor's glucose limitingmembrane, HSA is human serum albumin, GOX is glucose oxidase enzyme(used as the catalyst), and Solution refers to the environment in whichthe electrode is disposed, such as, e.g., a user's bodily fluid(s).

In the ensuing discussion, the equivalent circuit model of FIG. 48 willbe used to explain some of the physical properties of the sensorbehavior. Nevertheless, it should be mentioned that, depending on howthe glucose diffusion is modeled, other circuit configurations may alsobe possible. In this regard, FIGS. 49A-49C show illustrations of someadditional circuit models, some of which include a larger number ofelements and/or parameters. For purposes of the instant discussion,however, it has been discovered that the circuit model of FIG. 48,wherein the mass transport limitation—i.e., the Warburg component—isattributed to glucose diffusion through the membrane, provides the bestfit vis-à-vis empirical data. FIG. 50A is a Nyquist plot showing thatthe equivalent circuit simulation 5020 fits the empirical data 5010 veryclosely. FIG. 50B is an enlarged diagram of the high-frequency portionof FIG. 50A, showing that the simulation tracks the actual sensor dataquite accurately in that region as well.

Each of the above-described circuit elements and parameters affects theEIS output in various ways. FIG. 51 shows a Nyquist plot, wherein Cdlincreases in the direction of Arrow A. As can be seen, as the value ofCdl increases, the length of the (lower frequency) Nyquist plotdecreases, and its slope increases. Thus, the length of the Nyquist plotdecreases from plot 5031 to plot 5039, with each of plots 5033, 5035,and 5037 having respective lengths that progressively decrease as Cdlincreases from plot 5031 to plot 5039. Conversely, the slope of theNyquist plot increases from plot 5031 to plot 5039, with each of plots5033, 5035, and 5037 having respective slopes that progressivelyincrease as Cdl increases from plot 5031 to plot 5039. Thehigher-frequency region of the Nyquist plot, however, is generally notaffected.

FIG. 52 shows a Nyquist plot, wherein α increases in the direction ofArrow A. Here, as a increases, the slope of the Nyquist plot increasesin the lower frequency region. In FIG. 53, as Rp increases in thedirection of Arrow A, the length and the slope of the lower-frequencyNyquist plot increase. The higher the Rp, the higher the amount ofresistance to the chemical reaction and, therefore, the slower the rateof electron and ion exchange. Thus, phenomenologically, FIG. 53 showsthat the length and the slope of the lower-frequency Nyquist plotincrease as the electron-ion exchange rate decreases—i.e., as theresistance to the chemical reaction increases, which, in turn, means alower current (Isig) output. Again, there is minimal to no effect on thehigher-frequency region of the Nyquist plot.

The effect of change in the Warburg admittance is shown in FIG. 54. Asthe Warburg admittance increases in the direction of Arrow A, both thelength and the slope of the lower-frequency Nyquist plot increase.Phenomenologically, this means that the length and the slope of thelower-frequency Nyquist plot tend to increase as the influx of thereactant increases. In FIG. 55, as λ increases in the direction of ArrowA, the slope of the Nyquist plot decreases.

In contrast to the above-described elements and parameters, themembrane-related elements and parameters generally affect thehigher-frequency region of the Nyquist plot. FIG. 56 shows the effect ofthe membrane capacitance on the Nyquist plot. As can be seen from FIG.56, changes in Cmem affect how much of the high-frequency region'ssemi-circle is visible. Thus, as membrane capacitance increases in thedirection of Arrow A, progressively less of the semi-circle can be seen.Similarly, as shown in FIG. 57, as the membrane resistance increases inthe direction of Arrow A, more of the high-frequency region semi-circlebecomes visible. In addition, as Rmem increases, the overall Nyquistplot shifts from left to right. The latter parallel-shifting phenomenonalso holds true for Rsol, as shown in FIG. 58.

The above discussion in connection with the equivalent circuit model ofFIG. 48 may be summarized as follows. First, Cdl, α, Rp, Warburg, and λgenerally control the low frequency response. More specifically, thelower-frequency Nyquist slope/Zimag primarily depends on Cdl, α, Rp, andλ, and the lower-frequency length/Zmagnitude primarily depends on Cdl,Rp, and Warburg Admittance. Second, Rmem and Cmem control thehigher-frequency response. In particular, Rmem determines the highfrequency semi-circle diameter, and Cmem determines the turning pointfrequency, having minimal overall effect on the Nyquist plot. Lastly,changes in Rmem and Rsol cause parallel shifts in the Nyquist plot.

FIGS. 59A-59C, 60A-60C, and 61A-61C show results of in-vitro experimentsfor changes in the above-described circuit elements during sensorstart-up and calibration. FIGS. 59A, 60A, and 61A are identical. Asshown in FIG. 59A, the experiments were generally run with two redundantworking electrodes 5050, 5060, and for a period of (between 7 and) 9days. A baseline glucose amount of 100 mg/dL was used, although thelatter was changed between zero and 400 mg/dL at various pointsthroughout the experiment (5070). In addition, the effects of a(solution) temperature change between 32° C. and 42° C. (5080) and a 0.1mg/dL acetaminophen response (5085) were explored. Lastly, theexperiments included an Oxygen stress test, where the supply of Oxygendissolved in the solution was varied (i.e., limited) between 0.1% and 5%(5075). For purposes of these experiments, a full EIS sweep (i.e., from0.1 Hz-8 kHz) was run, and the output data was recorded (and plotted)about once every 30 minutes. However, shorter or longer intervals mayalso be used.

In FIG. 59C, the sum of Rsol and Rmem—which, again, may be estimated bythe magnitude of real impedance at the inflection point of the Nyquistplot—displays a general downwards trend as a function of time. This isdue primarily to the fact that the membrane takes time to hydrate, suchthat, as time passes by, it will become less resistant to the electricalcharges. A slight correlation can also be seen between the plot for Isig(FIG. 59A) and that for Rsol+Rmem (FIG. 59C).

FIG. 60B shows the EIS output for Cdl. Here, there is initially arelatively rapid drop (5087), over a period of several hours, due to thesensor activation/sensor charge-up process. Thereafter, however, Cdlremains fairly constant, exhibiting a strong correlation with Isig (FIG.60A). Given the latter correlation, Cdl data, as an EIS parameter, maybe less useful in applications where glucose independence is desired. Asshown in FIG. 60C, the trend for Rp may be generally described as amirror image of the plot for Cdl. As the membrane becomes more hydrated,the influx increases, which is reflected in the plot of Warburgadmittance in FIG. 61B. As shown in FIG. 61C, λ remains generallyconstant throughout.

FIGS. 62-65 show the actual EIS response for various parts of theabove-described experiments. Specifically, the changes that were madeduring the first 3 days—i.e., glucose changes, Oxygen stress, andtemperature changes, as shown in FIGS. 59A, 60A, and 61A—are boxed(5091) in FIG. 62, with the Vcntr response 5093 being shown in thebottom portion of this Figure and in FIG. 59B. FIG. 63 shows that anIsig calibration via an increase in glucose caused the slope and lengthof the Nyquist plot to decrease. In FIG. 64, the Oxygen (or Vcntr)response is shown in Day 2, where Vcntr becomes more negative as theOxygen content is decreased. Here, the Nyquist plot becomes shorter inlength, and its slope decreases (5094), indicating a large decrease inimaginary impedance. The plot length depends primarily on Cdl and Rp,and is strongly correlated to Vcntr which, in turn, responds to changesin glucose and Oxygen. In FIG. 65, the Isig changes negligibly from Day2 to Day 3. Nevertheless, the Nyquist plot shifts horizontally (from theplot at 37° C.) for data taken at 32° C. (5095) and at 42° C. (5097).However, there is no significant impact on Nyquist plot length, slope,or Isig.

Putting the above-described EIS output and signature informationtogether: during sensor start-up, the magnitude of Rmem+Rsol decreasesover time, corresponding to a shift from right to left in the Nyquistplot. During this period, Cdl decreases, and Rp increases, with acorresponding increase in Nyquist slope. Finally, Warburg admittancealso increases. As noted previously, the foregoing is consistent withthe hydration process, with EIS plots and parameter values taking on theorder of 1-2 days (e.g., 24-36 hours) to stabilize.

Embodiments of the inventions described herein are also directed toreal-time self-calibration, and more particularly, to in-vivoself-calibration of glucose sensors based on EIS data. Any calibrationalgorithm, including self-calibration algorithms, must addresssensitivity loss. As discussed previously, two types of sensitivity lossmay occur: (1) Isig dip, which is a temporary loss of sensitivity,typically occurring during the first few days of sensor operation; and(2) permanent sensitivity loss, occurring generally at the end of sensorlife, and sometimes correlated with the presence of a Vcntr rail.

It has been discovered that sensitivity loss can manifest itself as anincrease in Rsol or Rmem (or both), which can be observed in the Nyquistplot as a parallel shift to the right, or, if Rmem changes, a morevisible start to a semicircle at the higher frequencies (resulting in anincrease in high-frequency imaginary impedance). In addition to, orinstead of, Rsol and Rmem, there could be an increase in Cmem only. Thiscan be observed as changes in the high-frequency semicircle. Sensitivityloss will be accompanied by a change in Cdl (by way of a longer tail inthe lower-frequency segment of the Nyquist plot). The foregoingsignatures provide a means for determining how different changes in EISoutput can be used to compensate for changes in sensitivity.

For a normally operating glucose sensor, there is a linear relationshipbetween blood glucose (BG) and the sensor's current output (Isig). Thus,

BG=CF×(Isig+c)

where “CF” is the Cal Factor, and “c” is the offset. This is shown inFIG. 66, where the calibration curve is as shown by line 6005, and “c”is the baseline offset 6007 (in nA). However, when there is an increasein Rmem and/or a decrease in Cmem, then c will be affected. Thus, line6009 depicts a situation in which Rmem increases and Cmemdecreases—which signifies changes in the membrane properties—therebycausing the offset “c” to move to 6011, i.e., a downward shift of thecalibration curve. Similarly, when there are (non-glucose related)changes in Cdl and increases in Rp—with a resultant increase in thelength of the (lower-frequency) Nyquist plot—then the slope will beaffected, where the slope=1/CF. Thus, in FIG. 66, line 6013 has adifferent (smaller) slope that line 6005. Combined changes can alsooccur, which is illustrated by line 6015, indicating sensitivity loss.

The length of the lower-frequency segment of the Nyquist plot(L_(nyquist))—which, for simplicity, may be illustratively estimated asthe length between 128 Hz and 0.105 Hz (real) impedance—is highlycorrelated with glucose changes. It has been discovered, through modelfitting, that the only parameter that changes during glucose changes isthe double layer capacitance Cdl, and specifically the double layeradmittance. Therefore the only Isig-dependent—and, by extension,glucose-dependent—parameter in the equivalent circuit model of FIG. 48is Cdl, with all other parameters being substantially Isig-independent.

In view of the above, in one embodiment, changes in Rmem and Cmem may betracked to arrive at a readjustment of the Cal Factor (BG/Isig) and,thereby, enable real-time self-calibration of sensors without the needfor continual finger-stick testing. This is possible, in part, becausechanges in Rmem and Cmem result in a change in the offset (c), but notin the slope, of the calibration curve. In other words, such changes inthe membrane-related parameters of the model generally indicate that thesensor is still capable of functioning properly.

Graphically, FIG. 67A shows actual blood glucose (BG) data 6055 that isbeing recorded, overlaid by the Isig output 6060 from the workingelectrode. Comparing the data from a first period (or time window)comprising approximately days 1-4 (6051) with the data from a secondperiod comprising approximately days 6-9 (6053), FIG. 67A shows that thesensor is drifting generally downwards during the second time period,indicating perhaps a moderate sensitivity loss in the sensor. There isalso an increase in Vcntr during the second time period, as shown inFIG. 67B.

With reference to FIGS. 68 and 69, it can be seen that the sensitivityloss is clearly shown by a rather significant increase in membraneresistance 6061, as well as a corresponding drop in Warburg Admittance6063, during the second time period between days 6 and 9. Accordingly,FIG. 70 shows that the calibration curve 6073 for the second time period6053 is parallel to, but shifted down from, the calibration curve 6071for the first time period 6051. Also, as discussed hereinabove inconnection with FIG. 57, as the membrane resistance (Rmem) increases,overall Nyquist plot shifts from left to right, and more of thehigh-frequency region semi-circle becomes visible. For the data of FIGS.67A-70, this phenomenon is shown in FIG. 71, where the enlargedhigher-frequency region of the Nyquist plot shows that the data from thesecond time period 6053 moves the plot from left to right as comparedwith the data from the first time period 6051, and that the semi-circlebecomes more and more visible (6080) as the shift in the Nyquist plotprogresses from left to right. In addition, the enlarged lower-frequencyregion of the plot shows that there is no significant change inL_(nyquist).

Changes in Cdl and Rp, on the other hand, generally indicate that theelectrode(s) may already be compromised, such that recovery may nolonger be possible. Still, changes in Cdl and Rp may also be tracked,e.g., as a diagnostic tool, to determine, based on the direction/trendof the change in these parameters, whether, the drift or sensitivityloss has in fact reached a point where proper sensor operation is nolonger recoverable or achievable. In this regard, in embodiments of theinvention, respective lower and/or upper thresholds, or ranges ofthresholds, may be calculated for each of Cdl and Rp, or for the changein slope, such that EIS output values for these parameters that falloutside of the respective threshold (range) may trigger, e.g.,termination and/or replacement of the sensor due to unrecoverablesensitivity loss. In specific embodiments, sensor-design and/orpatient-specific ranges or thresholds may be calculated, wherein theranges/thresholds may be, e.g., relative to the change in Cdl, Rp,and/or slope.

Graphically, FIG. 72A shows actual blood glucose (BG) data 6155 that isbeing recorded, overlaid by the Isig output from two working electrodes,WE1 6160 and WE2 6162. The graphs show data from a first time window forday 1 (6170), a second time window for days 3-5 (6172), a third timewindow for day 3 (6174), and a fourth time window for days 5½ to 9½(6176). Starting on Day 3, FIG. 72B shows that Vcntr rails at 1.2 volts.However, the decrease in sensitivity occurs from about Day 5 or so(6180). Once the Vcntr rails, the Cdl increases significantly, with acorresponding decrease in Rp, signifying a higher resistance to theoverall electrochemical reaction. As expected, the slope of thecalibration curve also changes (decreases), and L_(nyquist) becomesshorter (see FIGS. 73-75). It is noted that, in embodiments of theinventions herein, the occurrence of a Vcntr rail may be used to triggertermination of a sensor as unrecoverable.

The combined effect of the increase in membrane resistance, the decreasein Cdl, and Vcntr rail is shown in FIGS. 76A-76B and 77-80. In FIG. 76A,actual blood glucose (BG) data 6210 is overlaid by the Isig output fromtwo working electrodes, WE1 6203 and WE2 6205. As can be seen, WE1generally tracks the actual BG data 6210—i.e., WE1 is functioningnormally. The Isig from WE2, on the other hand, appears to start at alower point, and continues a downwards trend all the way from thebeginning to Day 10, thus signifying a gradual loss of sensitivity. Thisis consistent with the Cdl for WE2 (6215) being lower than that for WE1(6213), as shown in FIG. 77, even though the Cdl for both workingelectrodes generally exhibits a downward trend.

FIG. 79 shows the combined effect on the calibration curve, where boththe offset and the slope of the linear fit for the period of sensitivityloss (6235) change relative to the calibration curve 6231 for thenormally-functioning time windows. In addition, the Nyquist plot of FIG.80 shows that, in the lower-frequency region, the length of the Nyquistplot is longer where there is sensitivity loss (6245), as compared towhere the sensor is functioning normally (6241). Moreover, near theinflection point, the semicircles (6255) become more and more visiblewhere there is loss of sensitivity. Importantly, where there issensitivity loss, the Nyquist plot of FIG. 80 shifts horizontally fromleft to right as a function of time. In embodiments of the invention,the latter shift may be used as a measure for compensation orself-correction in the sensor.

Thus, as discussed herein, as an EIS signature, a temporary dip may becaused by increased membrane resistance (Rmem) and/or local Rsolincrease. An increase in Rmem, in turn, is reflected by increasedhigher-frequency imaginary impedance. This increase may be characterizedby the slope at high frequencies, (S_(nyquist))—which, for simplicity,may be illustratively estimated as the slope between 8 kHz and 128 Hz.In addition, Vcntr railing increases Cdl and decrease Rp, such that thelength and slope decrease; this may be followed by gradual Cdl decreaseand Rp increase associated with sensitivity loss. In general, a decreasein Cdl, combined with an increase in Rp (length increase) and in Rmemmay be sufficient to cause sensitivity loss.

In accordance with embodiments of the inventions herein, an algorithmfor sensor self-calibration based on the detection of sensitivity changeand/or loss is shown in FIG. 81. At blocks 6305 and 6315, a baselineNyquist plot length (L_(nyquist)) and a baseline higher frequency slope,respectively, are set, so as to be reflective of the EIS state at thebeginning of sensor life. As noted, the Nyquist plot length iscorrelated to the Cdl, and the higher frequency Nyquist slope iscorrelated to the membrane resistance. The process then continues bymonitoring the Nyquist plot length (6335) and the higher frequency slope(6345), as well as the Vcntr value (6325). When the Vcntr rails, thebaseline L_(nyquist) adjusted, or reset 6355, as the railing of theVcntr changes the Cdl significantly. There is therefore a feedback loop6358 to accommodate real-time changes in the monitored EIS parameters.

As shown in block 6375, as the length of the Nyquist plot is monitored,a significant increase in that length would indicate reducedsensitivity. In specific embodiments, sensor-design and/orpatient-specific ranges or thresholds may be calculated, wherein theranges/thresholds may be, e.g., relative to the change in the length ofthe Nyquist plot. Similarly, a more negative higher-frequency slopeS_(nyquist) corresponds to an increased appearance of the high-frequencysemicircle and would be indicative of a possible dip 6365. Any suchchanges in L_(nyquist) and S_(nyquist) are monitored, e.g., eithercontinuously or periodically and, based on the duration and trend of thereduction in sensitivity, a determination is made as to whether total(i.e., severe) sensitivity loss has occurred, such that specific sensorglucose (SG) value(s) should be discarded (6385). In block 6395, the CalFactor may be adjusted based on the monitored parameters, so as toprovide a “calibration-free” CGM sensor. It is noted that, within thecontext of the inventions herein, the term “calibration-free” does notmean that a particular sensor needs no calibration at all. Rather, itmeans that the sensor can self-calibrate (e.g., based on the EIS outputdata), in real time, and without the need for additional finger-stick ormeter data. In this sense, the self-calibration may also be referred toas “intelligent” calibration, as the calibration is not performed basedon a predetermined temporal schedule, but on an as-needed basis, inreal-time.

In embodiments of the inventions herein, algorithms for adjustment ofthe Cal Factor (CF) and/or offset may be based on the membraneresistance which, in turn, may be estimated by the sum of Rmem and Rsol.As membrane resistance is representative of a physical property of thesensor, it generally cannot be estimated from EIS data run for a singlefrequency. Put another way, it has been observed that no singlefrequency will consistently represent membrane resistance, sincefrequencies shift depending on sensor state. Thus, FIG. 82, e.g., showsthat, when there is some sensitivity loss, there is a horizontal shiftin the Nyquist plot, and therefore, a shift in the inflection point thatestimates the value of Rmem+Rsol. In this case, the shift in the realcomponent of impedance is actually quite large. However, if only thehigh-frequency (e.g., at 8 kHz) real impedance is monitored, there islittle to no shift at all, as indicated by the encircled region in FIG.82.

There is therefore a need to track membrane resistance in a physicallymeaningful way. Ideally, this may be done through model fitting, whereRmem and Rsol are derived from model fitting, and Rm is calculated asRm=Rmem+Rsol. However, in practice, this approach is not onlycomputationally expensive, as it may take an unpredictably long amountof time, but also susceptible to not converging at all in somesituations. Heuristic metrics may therefore be developed to approximate,or estimate, the value of Rm=Rmem+Rsol. In one such metric, Rmem+Rsol isapproximated by the value of the real-impedance intercept at a fairlystable imaginary impedance value. Thus, as shown in FIG. 83, forexample, a region of general stability for the imaginary impedance (onthe Y axis) may be identified at about 2000Ω. Taking this as a referencevalue and traveling across, parallel to the X axis, a value proportionalto Rm may then be approximated as the real-impedance value of where thereference line crosses the Nyquist plot. An interpolation betweenfrequencies may be performed to estimate ΔRm∝Δ(Rmem+Rsol).

Having estimated the value of Rm as discussed above, the relationshipbetween Rm and the Cal Factor (CF) and/or Isig may then be explored.Specifically, FIG. 84 shows the relationship between the estimated Rmand CF, wherein the former is directly proportional to the latter. Thedata points for purposes of FIG. 84 were derived for steady state sensoroperation. FIG. 85 shows a plot of normalized Isig vs. 1/Rm, where Isighas been normalized by the BG range (of the Isig). As can be seen fromthe figure, Isig can be adjusted based on changes in Rm. Specifically,an increase in 1/Rm (i.e., reduced membrane resistance) will lead to aproportional increase in Isig, as there is a linear relationship betweenIsig and 1/Rm.

Thus, in one embodiment, an algorithm for adjustment of the Cal Factorwould entail monitoring the change in membrane resistance based on areference Cal Factor, and then modifying the Cal Factor proportionallybased on the correlation between Rm and CF. In other words:

$\left. {\frac{d({CF})}{dt} \propto \frac{d({Rm})}{dt}}\Rightarrow{{{Adjusted}\mspace{14mu} {CF}} \propto {\left( \frac{d({Rm})}{dt} \right) \times {CF}}} \right.$

In another embodiment, a Cal Factor adjustment algorithm may entailmodification of Isig based on proportional changes in 1/Rm, andindependently of CF calculations. Thus, for purposes of such analgorithm, the adjusted Isig is derived as

${{Adjusted}\mspace{14mu} {Isig}} \propto {\left( \frac{d\left( \frac{1}{R_{m}} \right)}{dt} \right) \times {Isig}}$

Experiments have shown that the most dramatic CF changes occur in first8 hours of sensor life. Specifically, in one set of in-vitroexperiments, Isig was plotted as a function of time, while keepingvarious glucose levels constant over the life of the sensor. EIS was runevery 3 minutes for the first 2 hours, while all model parameters wereestimated and tracked over time. As noted previously, given a limitedspectrum EIS, Rmem and Rsol cannot be (independently) estimatedrobustly. However, Rm=Rmem+Rsol can be estimated.

FIG. 86 shows the plots for Isig over time for various glucose levels,including 400 mg/dL (6410), 200 mg/dL (6420), 100 mg/dL (6430), 60 mg/dL(6440), and 0 mg/dL (6450). At startup, generally dramatic changesappear in all parameters. One example is shown in FIG. 87, where Cdl isplotted as a function of time, with plot 6415 corresponding to 400 mg/dLglucose, plot 6425 corresponding to 200 mg/dL glucose, plot 6435corresponding to 100 mg/dL glucose, plot 6445 corresponding to 60 mg/dLglucose, and plot 6455 corresponding to 0 mg/dL glucose. As is the casein the illustrative example of FIG. 87, most parameters correlate wellwith changes in the first 0.5 hour, but generally may not account forchanges in timeframes >0.5 hour.

It has been discovered, however, that Rm=Rmem+Rsol is the only parameterthat can account for changes in Isig over a similar startup time frame.Specifically, FIG. 88 shows the same graph as in FIG. 86, except for anindication that there is a peak, or second inflection point, that occursat about T=1 hour, especially at low glucose levels, e.g., 100 mg/dL andlower. However, of all the EIS parameters that were studied, membraneresistance was the only one that exhibited a relationship to this changein Isig; the other parameters generally tend to proceed fairly smoothlyto steady state. Thus, as shown in FIG. 89, Rm also exhibits a secondinflection point at about T=1 hour that corresponds to the peak in Isigat the same time.

FIG. 90 shows the relationship between Cal Factor and Rm for in-vivodata during the first 8 hours of sensor operation. Here, EIS was runabout once every 30 minutes at startup, and interpolated for periods inbetween. As can be seen, Rm=Rmem+Rsol correlates with Cal Factor (CF)during the first 8 hours of sensor operation. For purposes of thediagram in FIG. 90, the baseline offset was assumed to be 3 nA.

As noted above in connection with FIGS. 83-85, in one embodiment, analgorithm for adjustment of the Cal Factor at start up may includeselecting a reference value for the calibration factor (CF_(reference)),estimating the value of membrane resistance (R_(reference)) forCF=CF_(reference), monitoring the change in membrane resistance(Rm=Rmem+Rsol), and based on the magnitude of that change, adjusting thecalibration factor in accordance with the relationship shown in FIG. 90.Thus

CF(t)=CF _(reference) −m(R _(reference) −R _(m)(t))

where m is the gradient of the correlation in FIG. 90. It is noted that,for purposes of the above algorithm, the value of CF_(reference) issensor-specific, to account for the differences between sensors.

In another embodiment, the Cal Factor adjustment algorithm may bemodified by using a limited range of R_(m) over which adjustment occurs.This can help with small differences once R_(m) is smaller than ˜7000Ω,as may happen due to noise. The limited R_(m) range can also help whenR_(m) is very large, as may happen due to very slow sensorhydration/stabilization. In yet another embodiment, the range ofallowable CF may be limited, such as, e.g., by setting a lower limit of4.5 for CF.

FIG. 91A is a chart showing in-vivo results for MARD over all valid BGsin approximately the first 8 hours of sensor life. A single (first)calibration is performed with the first BG at either 1 hour, 1.5 hours,or 2 hours after startup. As can be seen, without any Cal Factoradjustment, the MARD for calibration at 1 hour is much higher than thatfor calibration performed at 2 hours (22.23 vs. 19.34). However, withadjustment, or modified adjustment, as described above, the differencebetween the respective MARD numbers becomes smaller. Thus, for example,with adjustment, the MARD for calibration at 1 hour is 16.98, ascompared to 15.42 for calibration performed at 2 hours. In addition, theMARD with adjustment for calibration at 1 hour is much less than theMARD without adjustment for calibration performed at 2 hours (16.98 vs.19.34). As such, in accordance with embodiments of the presentinvention, Cal Factor adjustments (and modified adjustments) may be usedto elongate the useable life of a sensor—e.g., by starting the sensorone hour earlier, in this example—while maintaining, or improving, theMARD. The chart in FIG. 91B provides median ARD numbers over all validBGs in approximately the first 8 hours.

FIGS. 92A-92C, 93A-93C, and 94A-94C show examples of when theabove-described Cal Factor adjustment algorithms work better than somecurrent, non-EIS based, methods. In one such method, generally referredto as “First Day Compensation” (or FDC), a first Cal Factor is measured.If the measured Cal Factor falls outside of a predetermined range, aconstant linear decay function is applied to bring the Cal Factor backto within normal range at a projected time determined by the rate of thedecay. As can be seen from FIGS. 92A-94C, the Cal Factor adjustmentalgorithms of the inventions herein (referred to in the diagrams as“Compensation”) 6701, 6711, 6721 produce results that are closer to theactual blood glucose (BG) measurements 6707, 6717, 6727 than resultsobtained by the FDC method 6703, 6713, 6723.

Given the complexities of estimating the value of EIS-relatedparameters, some of the current methods, including FDC, may becomputationally less complex than the EIS Cal Factor adjustmentalgorithms described herein. However, the two approaches may also beimplemented in a complementary fashion. Specifically, there may besituations in which FDC may be augmented by the instant Cal Factoradjustment algorithms. For example, the latter may be used to define therate of change of the FDC, or to identify the range for which FDC shouldbe applied (i.e., other than using CF alone), or to reverse thedirection of FDC in special cases.

In yet other embodiments, the offset, rather than the Cal Factor, may beadjusted. In addition, or instead, limits may be imposed on applicableranges of R and CF. In a specific embodiment, absolute, rather thanrelative, values may be used. Moreover, the relationship between CalFactor and membrane may be expressed as multiplicative, rather thanadditive. Thus,

$\frac{{CF}(t)}{{CF}_{reference}} = {- {m\left( \frac{R(t)}{R_{reference}} \right)}}$

In an embodiment using EIS-based dynamic offset, the total current thatis measured may be defined as the sum of the Faradaic current and thenon-Faradaic current, wherein the former is glucose-dependent, while thelatter is glucose-independent. Thus, mathematically,

i _(total) =i _(Faradaic) +i _(non-Faradaic)

Ideally, the non-Faradaic current should be zero, with a fixed workingpotential, such that

$i_{total} = {i_{Faradaic} = {A \times {Diffusivity} \times \frac{\partial C_{peroxide}}{\partial n}}}$

where A is the surface area,

$\frac{\partial C_{peroxide}}{\partial n}$

and ac is the gradient of Peroxide.

However, when the double layer capacitance in changing, the non-Faradaiccurrent cannot be ignored. Specifically, the non-Faradaic current may becalculated as

q_(non-Faradaic) = V × C = ∫_(t₀)^(t₀ + Δ t)i_(non-Faradaic)dt${\frac{d}{dt}q_{{non}\text{-}{Faradaic}}} = {i_{{non}\text{-}{Faradaic}} = {\frac{d\left( {V \times C} \right)}{dt} = {{C\; \frac{dV}{dt}} + {V\frac{dC}{dt}}}}}$

where q is the charge, V is the voltage, C is (double layer)capacitance. As can be seen from the above, when both voltage (V) andcapacitance (C) are constant, both time-derivative values on theright-hand side of the equation are equal to zero, such thati_(non-Faradaic)=0. In such an ideal situation, the focus can then turnto diffusion and reaction.

When V and C are both functions of time (e.g., at sensorinitialization),

$i_{{non}\text{-}{Faradaic}} = {\frac{d\left( {V \times C} \right)}{dt} = {{C\; \frac{dV}{dt}} + {V\frac{dC}{dt}}}}$

On the other hand, when V is constant, and C is a function of time,

$i_{{non}\text{-}{Faradaic}} = {V\frac{dC}{dt}}$

Such conditions are present, for example, on day 1 of sensor operation.FIG. 95 shows an example of a typical (initial) decay in double layercapacitance during day 1, in this case, the first 6 hours after sensorinsertion. As indicated on the graph, plot 6805 shows raw Cdl data basedon EIS data obtained at half-hour intervals, plot 6810 shows a splinefit on the raw Cdl data for 5-minute time intervals, plot 6815 shows thesmoothed curve for 5-minute time intervals, and plot 6820 shows apolynomial fit on the smoothed Cdl data for 5-minute time intervals.

It is noted that the Cdl decay is not exponential. As such, the decaycannot be simulated with an exponential function. Rather, it has beenfound that a 6^(th)-order polynomial fit (6820) provides a reasonablesimulation. Thus, for the purposes of the above-mentioned scenario,where V is constant and C is a function of time, i_(non-Faradaic) may becalculated if the polynomial coefficients are known. Specifically,

C=P(1)t ⁶ +P(2)t ⁵ +P(3)t ⁴ +P(4)t ³ +P(5)t ² +P(6)t ¹ +P(7)

where P is the polynomial coefficient array, and t is time. Thenon-Faradaic current can then be calculated as:

$i_{{non}\text{-}{Faradaic}} = {{V\frac{dC}{dt}} = {V\left( {{6{P(1)}t^{5}} + {5{P(2)}t^{4}} + {4{P(3)}t^{3}} + {3{P(4)}t^{2}} + {2{P(5)}t^{1}} + {P(6)}} \right)}}$

Finally, since i_(total)=iFaradaic+i_(non-Faradaic), the non-Faradaiccomponent of the current can be removed by rearranging, such that

i _(Faradaic) =i _(total) −i _(non-Faradaic)

FIG. 96 shows Isig based on the total current (6840), as a function oftime, as well as Isig after removal of the non-Faradaic current based onthe capacitance decay (6850). The non-Faradaic component of the currentmay be as high as 10-15 nA. As can be seen from the figure, removal ofthe non-Faradaic current helps remove a large majority of the lowstart-up Isig data at the beginning of sensor life.

It has been found that the above approach can be used to reduce theMARD, as well as adjust the Cal Factor right at the beginning of sensorlife. With regard to the latter, FIG. 97A shows the Cal Factor beforeremoval of the non-Faradaic current for a first working electrode (WE1)6860, and a second working electrode (WE2) 6870. FIG. 97B, on the otherhand, shows the Cal Factor for WE1 (6862) and WE2 (6872) after removalof the non-Faradaic current. Comparing the Cal Factor for WE1 in FIG.97A (6860) to that for WE1 in FIG. 97B (6862), it can be seen that, withremoval of the non-Faradaic component, the Cal Factor (6862) is muchcloser to the expected range.

In addition, the reduction in MARD can be seen in the example shown inFIGS. 98A and 98B, where sensor glucose values are plotted over time. Asshown in FIG. 98A, before removal of the non-Faradaic current,calibration at low startup causes significant sensor over-reading at WE1(6880), with a MARD of 11.23%. After removal of the non-Faradaiccurrent, a MARD of 10.53% is achieved for WE1. It is noted that, for theillustrative purposes of FIGS. 97A-98B, the non-Faradaic current wascalculated and removed in pre-processing using the relation

${i_{{non}\text{-}{Faradaic}} = {{V\frac{dC}{dt}} = {V\left( {{6{P(1)}t^{5}} + {5{P(2)}t^{4}} + {4{P(3)}t^{3}} + {3{P(4)}t^{2}} + {2{P(5)}t^{1}} + {P(6)}} \right)}}},$

where P is the polynomial coefficient (array) used to fit the doublelayer capacitance curve.

In real-time, separation of the Faradaic and non-Faradaic currents maybe used to automatically determine the time to conduct the firstcalibration. FIG. 99 shows the double layer capacitance decay over time.Specifically, over the constant time interval AT, the double layercapacitance undergoes a change from a first value C_(T) ₀ _(+ΔT) (7005)to a second value C_(T) (7010). A first-order time difference method,e.g., can then be used to calculate the non-Faradaic current as

$i_{{non}\text{-}{Faradaic}} = {{V\frac{dC}{dt}} \approx {V\frac{C_{T_{0} + {\Delta \; T}} - C_{T}}{\Delta \; T}}}$

Other methods may also be used to calculate the derivative

$\frac{dC}{dt},$

such as, e.g., second-order accurate finite value method (FVM),Savitzky-Golay, etc.

Next, the percentage of the total current, i.e., Isig, that is comprisedof the non-Faradaic current may be calculated simply as the ratioi_(non-Faradaic)/Isig. Once this ratio reaches a lower threshold, adetermination can then be made, in real-time, as to whether the sensoris ready for calibration. Thus, in one embodiment, the threshold may bebetween 5% and 10%.

In another embodiment, the above-described algorithm may be used tocalculate an offset value in real-time, i.e., an EIS-based dynamicoffset algorithm. Recalling that

$i_{{non} - {Faradaic}} = {{V\frac{dC}{dt}} = {V\left( {{6{P(1)}t^{5}} + {5{P(2)}t^{4}} + {4{P(3)}t^{3}} + {3{P(4)}t^{2}} + {2{P(5)}t^{1}} + {P(6)}} \right)}}$

and that sensor current Isig is the total current, including theFaradaic and non-Faradaic components

i _(total) =i _(Faradaic) +i _(non-Faradaic)

the Faradaic component is calculated as

i _(Faradaic) =i _(total) −i _(non-Faradaic)

Thus, in one embodiment, the non-Faradaic current, i_(non-Faradaic), canbe treated as an additional offset to Isig. In practice, when doublelayer capacitance decreases, e.g., during the first day of sensor life,i_(non-Faradaic) is negative, and decreases as a function of time.Therefore, in accordance with this embodiment of the invention, a largeroffset—i.e., the usual offset as calculated with current methods, plusi_(non-Faradaic)—would be added to the Isig at the very beginning ofsensor life, and allowed to decay following the 5^(th)-order polynomialcurve. That is, the additional offset i_(non-Faradaic) follows a5^(th)-order polynomial, the coefficient for which must be determined.Depending on how dramatic the change in double layer capacitance is, thealgorithm in accordance with this embodiment may apply to the first fewhours, e.g., the first 6-12 hours, of sensor life.

The polynomial fit may be calculated in various ways. For example, in anembodiment of the invention, coefficient P may be pre-determined basedupon existing data. Then, the dynamic offset discussed above is applied,but only when the first Cal Factor is above normal range, e.g., ˜7.Experiments have shown that, generally, this method works best when thereal-time double layer capacitance measurement is less reliable thandesired.

In an alternative embodiment, an in-line fitting algorithm is used.Specifically, an in-line double layer capacitance buffer is created attime T. P is then calculated based on the buffer, using a polynomial fitat time T. Lastly, the non-Faradaic current (dynamic offset) at timeT+ΔT is calculated using P at time T. It is noted that this algorithmrequires double layer capacitance measurements to be more frequent thantheir current level (every 30 mins), and that the measurements bereliable (i.e., no artifacts). For example, EIS measurements could betaken once every 5 minutes, or once every 10 minutes, for the first 2-3hours of sensor life.

In developing a real-time, self-calibrating sensor, the ultimate goal isto minimize, or eliminate altogether, the reliance on a BG meter. This,however, requires understanding of the relationships between EIS-relatedparameters and Isig, Cal Factor (CF), and offset, among others. Forexample, in-vivo experiments have shown that there is a correlationbetween Isig and each of Cdl and Warburg Admittance, such that each ofthe latter may be Isig-dependent (at least to some degree). In addition,it has been found that, in terms of factory calibration of sensors, Isigand Rm (=Rmem+Rsol) are the most important parameters (i.e.,contributing factors) for the Cal Factor, while Warburg Admittance, Cdl,and Vcntr are the most important parameters for the offset.

In in-vitro studies, metrics extracted from EIS (e.g., Rmem) tend toexhibit a strong correlation with Cal Factor. However, in-vivo, the samecorrelation can be weak. This is due, in part, to the fact thatpatient-specific, or (sensor) insertion-site-specific, properties maskthe aspects of the sensor that would allow use of EIS forself-calibration or factory calibration. In this regard, in certainembodiments, redundant sensors may be used to provide a reference pointthat can be utilized to estimate the patient-specific response. This, inturn, would allow a more robust factory calibration, as well as helpidentify the source of sensor failure mode(s) as either internal, orexternal, to the sensor.

In general, EIS is a function of electric fields that form between thesensor electrodes. The electric field can extend beyond the sensormembrane, and can probe into the properties of the (patient's) body atthe sensor insertion site. Therefore, if the environment in which thesensor is inserted/disposed is uniform across all tests, i.e., if thetissue composition is always the same in-vivo (or if the buffer isalways the same in-vitro), then EIS can be correlated to sensor-onlyproperties. In other words, it may be assumed that changes in the sensorlead directly to changes in the EIS, which can be correlated with, e.g.,the Cal Factor.

However, it is well known that the in-vivo environment is highlyvariable, as patient-specific tissue properties depend on thecomposition of the insertion site. For example, the conductivity of thetissue around the sensor depends on the amount of fat around it. It isknown that the conductivity of fat is much lower than that of pureinterstitial fluid (ISF), and the ratio of local fat to ISF can varysignificantly. The composition of the insertion site depends on the siteof insertion, depth of insertion, patient-specific body composition,etc. Thus, even though the sensor is the same, the Rmem that is observedfrom EIS studies varies much more significantly because the referenceenvironment is rarely, if ever, the same. That is, the conductivity ofthe insertion site affects the Rmem of the sensor/system. As such, itmay not be possible to use the Rmem uniformly and consistently as areliable calibration tool.

As described previously, EIS can also be used as a diagnostic tool.Thus, in embodiments of the inventions herein, EIS may be used for grossfailure analysis. For example, EIS can be used to detect severesensitivity loss which, in turn, is useful for determining whether, andwhen, to block sensor data, deciding on optimal calibration times, anddetermining whether, and when, to terminate a sensor. In this regard, itbears repeating that, in continuous glucose monitoring and analysis, twomajor types of severe sensitivity loss are typically considered: (1)Temporary sensitivity loss (i.e., an Isig dip), which typically occursearly in sensor life, and is generally believed to be a consequence ofexternal sensor blockage; and (2) Permanent sensitivity loss, whichtypically occurs at the end of sensor life, and never recovers, thusnecessitating sensor termination.

Both in-vivo and in-vitro data show that, during sensitivity loss andIsig dips, the EIS parameters that change may be any one or more ofRmem, Rsol, and Cmem. The latter changes, in turn, manifest themselvesas a parallel shift in the higher-frequency region of the Nyquist plot,and/or an increased appearance of the high-frequency semicircle. Ingeneral, the more severe the sensitivity loss, the more pronounced thesesymptoms are. FIG. 100 shows the higher-frequency region of the Nyquistplot for data at 2.6 days (7050), 3.5 days (7055), 6 days (7060), and6.5 days (7065). As can be seen, there may be a horizontal shift, i.e.,Rmem+Rsol shifts, from left to right, during sensitivity loss (7070),indicating an increase in membrane resistance. In addition, the plot for6 days, and especially that for 6.5 days (7065), clearly show theappearance of the higher frequency semicircle during sensitivity loss(7075), which is indicative of a change in membrane capacitance.Depending on the circumstances and the severity of the sensitivity loss,either or both of the above-mentioned manifestations may appear on theNyquist plot.

With specific regard to the detection of Isig dips, as opposed topermanent sensitivity loss, some current methodologies use the Isig onlyto detect Isig dips by, e.g., monitoring the rate at which Isig may bedropping, or the degree/lack of incremental change in Isig over time,thereby indicating that perhaps the sensor is not responsive to glucose.This, however, may not be very reliable, as there are instances whenIsig remains in the normal BG range, even when there is an actual dip.In such a situation, sensitivity loss (i.e., the Isig dip) is notdistinguishable from hypoglycemia. Thus, in one embodiment, EIS may beused to complement the information that is derived from the Isig,thereby increasing the specificity and sensitivity of the detectionmethod.

Permanent sensitivity loss may generally be associated with Vcntr rails.Here, some current sensor-termination methodologies rely solely on theVcntr rail data, such that, e.g., when Vcntr rails for one day, thesensor may be terminated. However, in accordance with embodiments of theinventions herein, one method of determining when to terminate a sensordue to sensitivity loss entails using EIS data to confirm whether, andwhen, sensitivity loss happens after Vcntr rails. Specifically, theparallel shift in the higher-frequency region of the Nyquist plot may beused to determine whether permanent sensitivity loss has actuallyoccurred once a Vcntr rail is observed. In this regard, there aresituations in which Vcntr may rail at, e.g., 5 days into sensor life,but the EIS data shows little to no shift at all in the Nyquist plot. Inthis case, normally, the sensor would have been terminated at 5-6 days.However, with EIS data indicating that there was, in fact, no permanentsensitivity loss, the sensor would not be terminated, thereby saving(i.e., using) the remainder of the sensor's useful life.

As mentioned previously, detection of sensitivity loss may be based onchange(s) in one or more EIS parameters. Thus, changes in membraneresistance (Rm=Rmem+Rsol), for example, may manifest themselves in themid-frequency (˜1 kHz) real impedance region. For membrane capacitance(Cmem), changes may be manifested in the higher-frequency (˜8 kHz)imaginary impedance because of increased semicircle. The double layercapacitance (Cdl) is proportional to average Isig. As such, it may beapproximated as the length of lower-frequency Nyquist slope L_(nyquist).Because Vcntr is correlated to oxygen levels, normal sensor behaviortypically entails a decrease in Vcntr with decreasing Isig. Therefore,an increase in Vcntr (i.e., more negative), in combination with adecrease in Isig may also be indicative of sensitivity loss. Inaddition, average Isig levels, rates of change, or variability of signalthat are low or physiologically unlikely may be monitored.

The EIS parameters must, nevertheless, be first determined. As describedpreviously in connection with Cal Factor adjustments and relateddisclosure, the most robust way of estimating the EIS parameters is toperform model fitting, where the parameters in model equations arevaried until the error between the measured EIS and the model output areminimized. Many methods of performing this estimate exist. However, fora real time application, model fitting may not be optimal because ofcomputational load, variability in estimation time, and situations whereconvergence is poor. Usually, the feasibility will depend on thehardware.

When the complete model fitting noted above is not possible, in oneembodiment, one method for real-time application is through use ofheuristic methodologies. The aim is to approximate the true parametervalues (or a corresponding metric that is proportional to trends shownby each parameter) with simple heuristic methods applied to the measuredEIS. In this regard, the following are implementations for estimatingchanges in each parameter.

Double Layer Capacitance (Cdl)

Generally speaking, a rough estimate of Cdl can be obtained from anystatistic that measures the length of the lower-frequency Nyquist slope(e.g., frequencies lower than ˜128 Hz). This can be done, for example,by measuring L_(nyquist) (the Cartesian distance between EIS at 128 Hzand 0.1 Hz in the Nyquist plot). Other frequency ranges may also beused. In another embodiment, Cdl may be estimated by using the amplitudeof the lower-frequency impedance (e.g., at 0.1 Hz).

Membrane Resistance (Rmem) and Solution Resistance (Rsol)

As has been discussed hereinabove, on the Nyquist plot, Rmem+Rsolcorresponds to the inflection point between the lower-frequency and thehigher-frequency semicircles. Thus, in one embodiment, Rmem+Rsol may beestimated by localizing the inflection point by detecting changes indirectionality of the Nyquist slope (e.g., by using derivatives and/ordifferences). Alternatively, a relative change in Rmem+Rsol can beestimated by measuring the shift in the Nyquist slope. To do this, areference point in the imaginary axis can be chosen (see FIG. 83) andinterpolation can be used to determine the corresponding point on thereal axis. This interpolated value can be used to track changes inRmem+Rsol over time. The chosen reference should lie within a range ofvalues that, for a given sensor configuration, are not overly affectedby large changes in the lower-frequency part of the Nyquist slope (forexample, because of Vcntr Rail). Typical values may be between 1 kΩ and3 kΩ. In another embodiment, it may be possible to use the realcomponent of a single high frequency EIS (e.g., 1 kHz, 8 kHz). Incertain sensor configurations, this may simulate Rmem the majority ofthe time, though it is noted that a single frequency may not be able torepresent Rmem exactly in all situations.

Membrane Capacitance (Cmem)

Increases in Cmem manifest as a more pronounced (or the more obviousappearance of) a higher-frequency semicircle. Changes in Cmem cantherefore be detected by estimating the presence of this semicircle.Thus, in one embodiment, Cmem may be estimated by tracking thehigher-frequency imaginary component of impedance. In this regard, amore negative value corresponds to the increased presence of asemicircle.

Alternatively, Cmem may be estimated by tracking the highest point inthe semicircle within a frequency range (e.g., 1 kHz-8 kHz). Thisfrequency range can also be determined by identifying the frequency atwhich the inflection point occurs, and obtaining the largest imaginaryimpedance for all frequencies higher than the identified frequency. Inthis regard, a more negative value corresponds to an increased presenceof the semicircle.

In a third embodiment, Cmem may be estimated by measuring the Cartesiandistance between two higher-frequency points in the Nyquist plot, suchas, e.g., 8 kHz and 1 kHz. This is the high frequency slope(S_(nyquist)) defined previously in the instant application. Here, alarger absolute value corresponds to an increased semicircle, and anegative slope (with negative imaginary impedance on the y axis, andpositive real impedance on the x) corresponds to the absence of asemicircle. It is noted that, in the above-described methodologies,there may be instances in which some of the detected changes in thesemicircle may also be attributed to changes in Rmem. However, becausechanges in either are indicative of sensitivity loss, the overlap isconsidered to be acceptable.

Non-EIS Related Metrics

For context, it is noted that, prior to the availability of EIS metrics,sensitivity loss was by and large detected according to several non-EIScriteria. By themselves, these metrics are not typically reliable enoughto achieve perfect sensitivity and specificity in the detection. Theycan, however, be combined with EIS-related metrics to provide supportingevidence for the existence of sensitivity loss. Some of these metricsinclude: (1) the amount of time that Isig is below a certain threshold(in nA), i.e., periods of “low Isig”; (2) the first order or secondorder derivatives of Isig leading to a state of “low Isig”, used as anindication of whether the changes in Isig are physiologically possibleor induced by sensitivity loss; and (3) the variability/variance of Isigover a “low Isig” period, which can be indicative of whether the sensoris responsive to glucose or is flat lining.

Sensitivity-Loss Detection Algorithms

Embodiments of the inventions herein are also directed to algorithms fordetection of sensitivity loss. The algorithms generally have access to avector of parameters estimated from EIS measurements (e.g., as describedhereinabove) and from non-EIS related metrics. Thus, e.g., the vectormay contain Rmem and or shift in horizontal axis (of the Nyquist plot),changes in Cmem, and changes in Cdl. Similarly, the vector may containdata on the period of time Isig is in a “low” state, variability inIsig, rates of change in Isig. This vector of parameters can be trackedover time, wherein the aim of the algorithm is to gather robust evidenceof sensitivity loss. In this context, “robust evidence” can be definedby, e.g., a voting system, a combined weighted metric, clustering,and/or machine learning.

Specifically, a voting system may entail monitoring of one or more ofthe EIS parameters. For example, in one embodiment, this involvesdetermining when more than a predetermined, or calculated, number of theelements in the parameter vector cross an absolute threshold. Inalternative embodiments, the threshold may be a relative (%) threshold.Similarly, the vector elements may be monitored to determine when aparticular combination of parameters in the vector crosses an absoluteor a relative threshold. In another embodiment, when any of a subset ofelements in the vector crosses an absolute or a relative threshold, acheck on the remainder of the parameters may be triggered to determineif enough evidence of sensitivity loss can be obtained. This is usefulwhen at least one of a subset of parameters is a necessary (but perhapsinsufficient) condition for sensitivity loss to be reliably detected.

A combined weighted metric entails weighing the elements in the vectoraccording to, for example, how much they cross a predetermined thresholdby. Sensitivity loss can then be detected (i.e., determined asoccurring) when the aggregate weighted metric crosses an absolute or arelative threshold.

Machine learning can be used as more sophisticated “black box”classifiers. For example, the parameter vector extracted from realisticin-vivo experimentation can be used to train artificial neural networks(ANN), support vector machines (SVM), or genetic algorithms to detectsensitivity loss. A trained network can then be applied in real time ina very time-efficient manner.

FIGS. 101A and 101B show two illustrative examples of flow diagrams forsensitivity-loss detection using combinatory logic. As shown, in bothmethodologies, one or more metrics 1-N may be monitored. In themethodology of FIG. 101A, each of the metrics is tracked to determine ifand when it crosses a threshold, and described hereinabove. The outputof the threshold-determination step is then aggregated via a combinatorylogic, and a decision regarding sensitivity loss is made based on theoutput of the combinatory logic. In FIG. 101B, values of the monitoredmetrics 1-N are first processed through a combinatory logic, and theaggregate output of the latter is then compared to a threshold value(s)to determine whether sensitivity loss has occurred.

Additional embodiments are also directed to using EIS in intelligentdiagnostic algorithms. Thus, in one embodiment, EIS data may be used todetermine whether the sensor is new, or whether it is being re-used (inaddition to methodologies presented previously in connection with re-useof sensors by patients). With regard to the latter, it is important toknow whether a sensor is new or is being re-used, as this informationhelps in the determination of what type of initialization sequence, ifany, should be used. In addition, the information allows prevention ofoff-label use of a sensor, as well as prevention of sensor damage due tomultiple reinitializations (i.e., each time a sensor is disconnected andthen re-connected, it “thinks” that it is a new sensor, and thereforetries to reinitialized upon re-connection). The information also helpsin post-processing of collected sensor data.

In connection with sensor re-use and/or re-connection, it has beendiscovered that the lower-frequency Nyquist slope for a new sensorbefore initialization is different from (i.e., lower than) thelower-frequency Nyquist slope for a sensor that has been disconnected,and then reconnected again. Specifically, in-vitro experiments haveshown that the Nyquist slope is higher for a re-used sensor as opposedto a newly-inserted one. The Nyquist slope, therefore, can be used as amarker to differentiate between new and used (or re-used) sensors. Inone embodiment, a threshold may be used to determine, based on theNyquist slope, whether a specific sensor is being re-used. In oneembodiment, the threshold may be a Nyquist slope=3. FIG. 102 shows thelow-frequency Nyquist plot with a reference slope=3 (8030), as well asthe plots for a new sensor (pre-initialization) 8010, a new sensor(post-initialization) 8015, a reconnected sensor (pre-initialization)8020, and a reconnected sensor (post-initialization) 8020. As noted, theslope for a new sensor (pre-initialization) 8010 is lower than thereference, or threshold (8030), while that for a reconnected sensor(pre-initialization) 8020 is higher than the threshold (8030).

In another embodiment, EIS data may be used to determine the type ofsensor being used. Here, it has been discovered that, if the sensordesigns are significantly different, the respective EIS outputs shouldalso be significantly different, on average. Different sensorconfigurations have different model parameters. It is therefore possibleto use identification of these parameters at any point during the sensorlife to determine the sensor type currently inserted. The parameters canbe estimated, e.g., based on methods described hereinabove in connectionwith gross failure/sensitivity-loss analysis. Identification can bebased on common methods to separate values, for example, settingthresholds on specific (single or multiple) parameters, machine learning(ANN, SVM), or a combination of both methods.

This information may be used, e.g., to change algorithm parameters andinitialization sequences. Thus, at the beginning of the sensor life,this can be used to have a single processing unit (GST, GSR) to setoptimal parameters for the calibration algorithm. Offline (nonreal-time), the identification of sensor type can be used to aidanalysis/evaluation of on-the-field sensor performance.

It has also been discovered that the length of the lower-frequencyNyquist slope may be used to differentiate between different sensortypes. FIGS. 103A-103C show Nyquist plots for three different sensors(i.e., different sensor configurations), identified as Enlite (8050),Enlite 2 (i.e., “Enlite Enhanced”) (8060), and Enlite 3 (8070), all ofwhich are manufactured by Medtronic Minimed (Northridge, Calif.). As canbe seen, for various stages, including pre-initialization,post-initialization, and second post-initialization (FIGS. 103A-103C,respectively), the Enlite sensor has the shortest lower-frequencyNyquist slope length (8050), followed by the Enlite 2 (8060), and theEnlite 3 (8070), which has the longest length. The latter are also shownon FIG. 104, where Nyquist (slope) length, computed as the Cartesiandistance between EIS at 0.105 Hz and 1 Hz, is plotted against time.

Embodiments of the inventions herein are also directed to usingdiagnostic EIS measurements as a guide in determining the type ofinitialization that should be performed. As noted previously,initialization sequences can be varied based on detected sensor type(EIS-based or other), and/or detection of whether a new or old sensor isinserted (EIS-based). In addition, however, EIS-based diagnostics mayalso be used in determining a minimal hydration state prior toinitialization (e.g., by tracking Warburg impedance), or in determiningwhen to terminate initialization (e.g., by tracking reaction-dependentparameter, such as, e.g., Rp, Cdl, Alpha, etc.), so as to properlyminimize sensor initialization time.

More specifically, to minimize initialization response time, additionaldiagnostics are required to control the processes that occur duringinitialization. In this regard, EIS may provide for the requiredadditional diagnostics. Thus, for example, EIS may be measured betweeneach initialization pulse to determine if further pulsing is required.Alternatively, or in addition, EIS may be measured during high pulses,and compared to the EIS of optimal initialization state to determinewhen the sensor is sufficiently initialized. Lastly, as noted above, EISmay be used in estimating a particular model parameter—most likely oneor more reaction-dependent parameters, such as Rp, Cdl, Alpha, etc.

As has been noted, sensor calibration in general, and real-time sensorcalibration in particular, is central to a robust continuous glucosemonitoring (CGM) system. In this regard, calibration algorithms aregenerally designed such that, once a BG is received by taking afingerstick, the new BG value is used to either generate an errormessage, or update the calibration factor which, in turn, is used tocalculate sensor glucose. In some previous algorithms, however, a delayof 10-20 minutes may exist between the time when a fingerstick isentered, and the time when the user is notified of either thefingerstick being accepted or a new fingerstick being required forcalibration. This is burdensome, as the user is left not knowing whetherhe/she will need his/her BG meter again in a few minutes.

In addition, in some situations, the presence of older BG values in thecalibration buffer causes either perceived system delay, due to thenewest BG value carrying less than 100% weight, or inaccuracy in thecalculated SG (due to the older BG values no longer being representativeof the current state of the system). Moreover, erroneous BG values aresometimes entered, but not caught by the system, which may lead to largeinaccuracies until the next calibration.

In view of the above, embodiments of the inventions herein seek toaddress potential shortcomings in prior methodologies, especially withregard to sensor performance for use with closed-loop systems. Forexample, in order to make the system more predictable, calibrationerrors may be notified only when the fingerstick (BG value) is receivedby the transmitter (i.e., entered), rather than, e.g., 10-15 minuteslater. Additionally, in contrast to some existing systems, where aconstant calibration error (CE) threshold is used, certain embodimentsherein may utilize variable calibration error thresholds when highererrors are expected (e.g., either due to lower reliability of thesensor, or high rates of change), thereby preventing unnecessarycalibration error alarms and fingerstick requests. Thus, in one aspect,when the sensor is in FDC mode, Isig dip calibration mode, or undergoinga high rate of change (e.g., when 2-packet rate of change×CF>1.5mg/dL/min.), a limit corresponding to 50% or 50 mg/dL may be used.

On the other hand, when low error is expected, the system may use atighter calibration error limit, such as, e.g., 40% or 40 mg/dL. Thisreduces the likelihood that erroneous BG values may be used forcalibration, while also allowing the status of the calibration attemptto be issued immediately (i.e., accepted for calibration, or acalibration error). Moreover, in order to handle situations where newerIsig values would cause a calibration error, a check at calibration time(e.g., 5-10 minutes after fingerstick) may select the most appropriatefiltered Isig (fIsig) value to use for calibration.

In connection with the aforementioned issues involving BG values and theBG buffer, embodiments of the inventions herein aim to reduce the delay,and the perceptions of delay, by assigning higher weighting to the newerBG value than was assigned in previous algorithms, and by ensuring thatthe early calibration update occurs more frequently. In addition, insituations where there is a confirmed sensitivity change (as confirmed,e.g., by the Smart Calibration logic mentioned previously and to beexplored hereinbelow, and by recent calibration BG/Isig ratios), thecalibration buffer may undergo partial clearing. Lastly, whereas prioralgorithms may have employed an expected calibration factor (CF) weightwhich was a constant, embodiments of the invention provide for avariable CF value based on sensor age.

In short, variable calibration error thresholds may be provided based onexpectation of error during calibration attempt, as well as issuance ofcalibration error message(s) without waiting for additional sensor data,less delay in calibrating (e.g., 5-10 minutes), updated expectedcalibration factor value based on sensor age, and partial clearing ofthe calibration buffer as appropriate. Specifically, in connection withFirst Day Compensation (FDC), embodiments of the inventions hereinprovide for requesting additional calibrations when higher Cal Factorthresholds are triggered in order to more expeditiously correct sensorperformance. Such higher CF thresholds may be set at, e.g., between 7and 16 mg/dL/nA, with the latter serving as the threshold for indicationof calibration error in some embodiments.

Thus, in one aspect, if a high CF threshold is triggered after the firstcalibration, the system requires that the next calibration be performedin 3 hours. However, if a high CF threshold is triggered after thesecond, or subsequent, calibration, the system requires that the nextcalibration be performed in 6 hours. The foregoing procedure may beimplemented for a period of 12 hours from sensor connection.

In another aspect, the expected Cal Factor, which is used duringcalibration to calculate the Cal Factor, is increased over time so as toreduce the likelihood of under-reading. By way of background, existingmethodologies may use a fixed expected Cal Factor throughout the sensorlife, without accounting for possible shifts in sensor sensitivity. Insuch methodologies, the expected Cal Factor may be weighted incalculating the final Cal Factor, and used to reduce noise.

In embodiments of the inventions herein, however, the expected CF iscalculated as a function of time, expressed in terms of the age of thesensor. Specifically,

${{Expected}\mspace{14mu} {CF}} = {{{SensorAge} \times \frac{0.109\mspace{14mu} {mg}\text{/}{dL}\text{/}{nA}}{day}} + {4.730\mspace{14mu} {mg}\text{/}{dL}\text{/}{nA}}}$

where Sensor Age is expressed in units of days. In further embodiments,the expected Cal Factor may be calculated as a function of the existingCF and impedance, such that any changes in sensitivity may be reflectedin the expected CF. In addition, in aspects of the invention, expectedCF may be calculated on every Isig packet, rather than doing so only ata BG entry, so as to gradually adjust the Cal Factor betweencalibrations.

In connection with calibration buffer and calibration errorcalculations, certain embodiments provide for modification ofcalibration buffer weights and/or clearing of the calibration buffer.Specifically, when impedance measurements (e.g., through EIS) indicatethat the Cal Factor might have changed, and a calibration attemptindicates that a change might have occurred, the change in Cal Ratio(CR) is checked by comparing the CR of the current BG to the most recentCR in the calibration buffer. Here, such a change may be verified by,e.g., values of the 1 kHz impedance, as detailed previously inconnection with related EIS procedures. In addition, weights may beadded in the calibration buffer calculation based on reliabilityindices, the direction in which the Cal Factor is expected to change,and/or the rate of change of calibration. In the latter situation, e.g.,a lower weight may be assigned, or CF only temporarily updated, ifcalibration is on a high rate of change.

In embodiments of the inventions herein, selection of filtered Isig(fIsig) values for the calibration buffer may be initiated on the secondIsig packet after BG entry. Specifically, the most recent of the pastthree (3) fIsig values that would not cause a calibration error may beselected. Then, once accepted for calibration, the calibration processwill proceed without a calibration error being issued. Such calibrationerror may be caused, e.g., by an invalid Isig value, a Cal Ratio rangecheck, a percentage error check, etc.

In other embodiments, values of fIsig may be interpolated to derive aone minute resolution. Alternatively, fIsig values may be selected fromrecent values based on the rate of change in the values (and accountingfor delays). In yet another alternative embodiment, fIsig values may beselected based on a value of CR that is closest to a predicted CR value.The predicted CR value, in turn, is closest to the current value of theCal Factor, unless the latter, or EIS data, indicate that CF shouldchange.

As noted previously, in connection with FIGS. 24 and 34, e.g., valuesfor 1 kHz real impedance provide information on potential occlusion(s)that may exist on the sensor membrane surface, which occlusion(s) maytemporarily block passage of glucose into the sensor and thus cause thesignal to dip. More broadly, the 1 kHz real impedance measurement may beused to detect sensor events that are typically sudden, and may indicatethat the sensor is no longer fully inserted. In this regard, FIG. 105shows a flow chart for a method of blanking sensor data or terminatingthe sensor in accordance with one embodiment.

The methodology starts at block 9005, where 1 kHz real impedance valuesare filtered using, e.g., a moving average filter, and, based thereon, adetermination is made as to whether the EIS-derived values are stable(9010). If it is determined that the EIS-derived values are not stable,the methodology proceeds to block 9015, wherein a further determinationis made based on the magnitude of the 1 kHz impedance. Specifically, ifboth the filtered and unfiltered values of 1 kHz real impedance are lessthan 7,000Ω, then EIS is set as stable (9020). If, on the other hand,both the filtered and unfiltered values of 1 kHz real impedance are notless than 7,000Ω, then EIS is set as unstable (9025). It is noted thatthe above-described 7,000Ω threshold prevents data blanking or sensortermination for sensors that have not stabilized.

When EIS is stable, the algorithm proceeds to block 9030. Here, if the 1kHz real impedance is less than 12,000Ω (9030), and also less than10,000Ω (9040), the algorithm determines that the sensor is withinnormal operating range and, as such, allows sensor data to continue tobe displayed (9045). If, on the other hand, the 1 kHz real impedancevalue is greater than 10,000Ω (i.e., when the 1 kHz real impedance isbetween 10 kΩ and 12 kΩ), the logic determines whether the 1 kHz realimpedance value has been high (i.e., greater than 10 kΩ) for the past 3hours (9050). If it is determined that the 1 kHz real impedance valuehas been high for the past 3 hours, then the sensor is terminated at9060, as the sensor is assumed to have pulled out, rendering sensor datainvalid. Otherwise, the sensor is not terminated, as the sensor signalmay be simply drifting, which, as discussed previously, may be arecoverable phenomenon. Nevertheless, the sensor data is blanked (9055)while the sensor is given a chance to recover.

It is noted that, in further embodiments, in determining whether datashould be blanked, or the sensor terminated, the logic may alsoconsider, in addition to the above-mentioned thresholds, suddenincreases in impedance by, e.g., comparing impedance derivatives tohistorical derivatives. Moreover, the algorithm may incorporatenoise-based blanking or termination, depending on the duration of highnoise-low sensor signal combination. In this regard, prior methodologiesincluded termination of the sensor after three (3) consecutive 2-hourwindows of high noise and low sensor signal. However, in order toprevent unreliable data from being displayed to the user, embodimentsherein employ noise-based blanking, wherein the algorithm stopscalculating SG values after 2 consecutive 2-hour windows (i.e., at thestart of the third consecutive window) involving high noise and lowsignal. In further aspects, the algorithm may allow further calculationand display of the calculated SG values after one hour of blanking,rather than two hours, where the sensor signal appears to haverecovered. This is an improvement over methodologies that blankotherwise reliable data for longer periods of time.

Whereas 1 kHz real impedance may be used to detect sudden sensorfailures, measurements of imaginary impedance at higher frequencies(e.g., 8 kHz) may be used to detect more gradual changes, where sensorsensitivity has drifted significantly from its typical sensitivity. Inthis regard, it has been discovered that a large shift in 8 kHzimaginary impedance typically signifies that the sensor has experienceda large change in glucose sensitivity, or is no longer stable.

FIG. 106 shows a flow diagram for a method of sensor termination inaccordance with an embodiment of the inventions herein. As shown in FIG.106, the algorithm employs a reference at 1.5 days (since sensor start),as doing so provides for a more robust logic, and ensures that the logicfocuses on long-term sensitivity changes. Thus, if the sensor has notbeen operating for at least 1.5 days (9002), no action is taken, and thealgorithm “waits” (9012), i.e., it periodically loops back to step 9002.Once the condition in block 9002 is met, a determination is made as towhether a reference imaginary impedance value is set (9022). If areference value has not been previously set, the algorithm proceeds toset one by assigning the minimum 8 kHz imaginary impedance value sincesensor initialization as the reference value (9032), clipped within therange −1,000Ω-800Ω. With the reference value set, a change value iscalculated as the absolute value of the difference between the referencevalue and the current value of the 8 kHz imaginary impedance (9052). Inblock 9062, the algorithm determines whether the change value is greaterthan 1,200Ω for two consecutive measurements, as well as whether the CalRatio is larger than 14. If at least one of the latter inquiries isanswered in the negative, then the sensor is allowed to continueoperating and display SG values (9072). However, if the change value isgreater than 1,200Ω for two consecutive measurements, and the Cal Ratiois larger than 14, then the sensor is terminated at block 9082.

Embodiments of the inventions herein are also directed to assessment ofreliability of sensor glucose values, as well as estimation ofsensor-data error direction, in order to provide users and automatedinsulin delivery systems—including those in closed-loop systems—anindicator of how reliable the system is when SG is displayed to theuser. Depending on the reliability of sensor data, such automatedsystems are then able to assign a corresponding weight to the SG, andmake a determination as to how aggressively treatments should beprovided to users. Additionally, the direction of error can also be usedto inform users and/or the insulin delivery system in connection with SGbeing a “false low” or a “false high” value. The foregoing may beachieved by, e.g., detecting dips in sensor data during the first day(EIS dip detection), detecting sensor lag, and lower-frequency (e.g., 10Hz) impedance changes.

Specifically, in accordance with one embodiment, it has been discoveredthat a Cal Factor (CF) of above about 9 mg/dL/nA may be indicative oflow sensor reliability and, as such, a predictor of higher error. Thus,CF values outside of this range may be generally indicative of one ormore of the following: abnormal glucose sensitivity; calibrations thatoccurred during a dip in signal; delay in entering BG information, orhigh rate of change when calibrating; BG error when calibrating; andsensor with a transient change in glucose sensitivity.

FIG. 107 shows a flow diagram for a signal dip detection methodology inaccordance with an embodiment of the invention, where increases inunfiltered real 1 kHz impedance may be used in combination with low Isigvalues to identify the start of a dip. As shown in the diagram, at block9102, the logic determines whether sensor data is currently beingblanked due to signal dip. If data is not being blanked, then the logicdetermines whether less than 4 hours have passed since sensor start(9104). If more than 4 hours have elapsed since sensor start, the logicthen determines whether more than 12 hours have passed since sensorstart (9106), in which case there will be no dip detection or blankingof data (9108). Thus, in this regard, the methodology is directed toidentifying transient dips during the first 12 hours of sensor data.

Returning to block 9106, if less than 12 hours have passed since sensorstart, then an inquiry is made regarding the recent EIS, Isig, and SGvalues. Specifically, in block 9110, if the two most-recent realimpedance values (at 1 kHz) have been increasing, Isig<18 nA, and SG<80mg/dL, then the algorithm determines that the start of a dip has beendetected, and notifies the system to stop displaying SG values (9112).On the other hand, if all of the foregoing conditions are not met, thenthere will be no dip detection or data blanking (9108).

When it is determined, at block 9104, that less than 4 hours have passedsince sensor start, then a sensor dip event may still be encountered.Specifically, if the two most-recent EIS (i.e., 1 kHz impedance) valuesare increasing, and Isig<25 nA, then the algorithm determines that thestart of a dip has been detected, and notifies the system to stopdisplaying SG values (9114, 9116). If, however, the two most-recent 1kHz impedance values are not increasing, or Isig is not less than 25 nA,then there will be no dip detection or data blanking (9108), as before.

Returning to block 9102, if it is determined that data is currentlybeing blanked due to a dip, there is still a possibility that data willnevertheless be shown. That is, if Isig is greater than about 1.2 timesIsig at the start of the dip event (9118), then it is determined thatIsig has recovered, i.e., the dip event is over, and data display willresume (9122). On the other hand, if Isig is not greater than about 1.2times Isig at the start of the dip event (9118), then it is determinedthat Isig has not yet recovered, i.e., the dip event is not over, andthe system will continue to blank sensor data (9120).

In accordance with embodiments of the inventions herein, the directionof error in SG (under-reading or over reading), in general, may bedetermined by considering one or more factors related to under- and/orover-reading. Thus, it has been discovered that under-reading in sensorsmay occur when: (1) Vcntr is extreme (e.g., Vcntr<−1.0 V); (2) CF ishigh (e.g., CF>9); (3) lower frequency impedance (e.g., at 10 Hz) ishigh (e.g., real 10 Hz impedance>10.2 kΩ); (4) FDC is in low CF mode;(5) sensor lag suggests under-reading; (6) lower frequency impedance(e.g., at 10 Hz) increases (e.g., 10 Hz impedance increases over 7000);and/or (7) EIS has detected a dip. Over-reading, on the other hand, mayoccur when: (1) lower frequency impedance (e.g., 10 Hz) decreases (e.g.,lower frequency impedance<−200Ω); (2) sensor lag suggests over-reading;and/or (3) FDC when CF is in extreme mode.

Such under-reading or over-reading, especially in closed-loop systems,can have a profound impact on patient safety. For example, over-readingnear the hypoglycemic range (i.e., <70 mg/dL) may cause an overdose ofinsulin to be administered to the patient. In this regard, severalindicators of error direction have been identified, which may be used astest criteria, including: (1) low sensitivity indicators; (2) sensorlag; (3) FDC mode; and (4) loss/gain in sensitivity since calibration.

Two such low sensitivity indicators are high (lower-frequency) realimpedance (e.g., >10 kΩ) and high Vcntr (e.g., Vcntr<−1.0V), both ofwhich are, in general, indicative of loss of sensitivity. FIG. 108Ashows an example in which Vcntr 9130 gradually increases (i.e., becomesmore negative) as a function of time. At about 115 hours, shown by line9135, Vcntr crosses—1.0V, as indicated by line 9137, and continues toincrease (i.e., Vcntr<−1.0V) to about −1.2V. As shown, prior to about115 hours, the Isig trend 9132 generally follows the Vcntr trend.However, once Vcntr passes the threshold (i.e., to the right of line9135), the Isig departs from Vcntr, and continues to drop. At the sametime, as shown in FIG. 108B, glucose 9134 also has a generally downwardtrend, with Cal errors 9136 being indicated at about 130 hours and about165 hours.

As discussed previously, (EIS) sensor dips are also indicative oftemporary sensitivity loss. Similarly, a high Cal Factor is indicativeof the sensor's attempt to compensate for reduced sensitivity. In oneexample shown in FIGS. 109A and 109B, the Cal Factor 9140 increasessteadily as a function of time. At about 120 hours (9145), the CalFactor 9140 crosses a threshold value of 9 (9147). As shown in FIG.109B, once the Cal Factor crosses the threshold, the glucose values 9142show more frequent departures from BG values, with several errors 9144occurring between about 135 hours and 170 hours.

As mentioned previously, sensor lag is another indicator of errordirection. Accordingly, in an embodiment of the inventions herein, theerror that is caused by sensor lag is compensated for by approximatingwhat the glucose value will be. Specifically, in one embodiment, theerror from sensor lag may be approximated by defining:

sg(t+h)=sg(t)+hsg′(t)+½sg″(t)

where sg(t) is the sensor glucose function, and “h” is the sensor lag.The error may then be calculated as

${Error} = {\frac{{{sg}\left( {t + h} \right)} - {{sg}(t)}}{{sg}(t)} = \frac{\left( {{{hsg}^{\prime}(t)} + {\frac{1}{2}h^{2}{{sg}^{''}(t)}}} \right)}{{sg}(t)}}$or${Error} = {\frac{k\left( {{C_{1}{{sg}^{\prime}(t)}} + {C_{2}{{sg}^{''}(t)}}} \right)}{{sg}(t)}.}$

First day calibration (FDC) occurs when the Cal Factor (CF) is notwithin the expected range. The CF is set to the value indicated by thecalibration, and then ramps up or down to the expected range, as shown,e.g., in FIGS. 110A and 110B. During this time, usually high, butgenerally predictable, errors may exist, resulting in potentialover-reads or under-reads. As can be seen from FIGS. 110A and 110B, theCF changes at a generally constant slope as it rises or falls, and thensettles, in this case at 4.5 or 5.5.

Lastly, post-calibration sensitivity change, i.e., loss/gain insensitivity since calibration, is also an indicator of error/errordirection. Under normal circumstances, and except for first daycalibration as discussed hereinabove, the Cal Factor remains generallyconstant until a new calibration is performed. Shifts in sensitivityafter calibration, therefore, can cause over-reads and under-readswhich, in turn, may be reflected by values of lower-frequency (e.g., 10Hz) real impedance.

Specifically, it has been discovered that a drop in lower-frequency realimpedance causes over-reading, with the direction of error beingindicated by the real impedance curve. Conversely, lower-frequencyreal-impedance increases cause under-reading, with the direction oferror also being indicated by the real impedance curve. However, currentdirectionality tests may be unable to readily decipher points at peaksand valleys of the glucose profile. Thus, in one embodiment, the degreeof sharpness of such peaks and valleys may be reduced by filtering, suchas, e.g., by deconvolution with lowpass filtering.

As described previously in connection with FIG. 81, e.g., sensitivitychange and/or loss may be used to inform proper sensor calibration. Inthis regard, in a further aspect of the inventions herein, changes insensor sensitivity may be predicted based on the previous calibrationfactor or on impedance so as to enable implementation of “smartcalibrations”, which help address continued generation and/or display ofinaccurate glucose data when, e.g., sensor sensitivity has changed.

It is known that, in some existing continuous glucose monitoring systems(CGMS), calibration fingersticks are required every twelve hours. Thecalibration allows the CGMS to update the function used to convert themeasured sensor current into a displayed glucose concentration value. Insuch systems, the 12-hour calibration interval is selected as a balancebetween reducing the user burden (of performing too many fingersticks)and using an interval that is sufficient to adjust for changes in sensorsensitivity before inaccuracies can cause too large of a problem.However, while this interval may be appropriate in general, if thesensor sensitivity has changed, 12 hours can be too long to wait if ahigh level of accuracy (in support of closed loop insulin delivery) isexpected.

Embodiments of the inventions herein, therefore, address the foregoingissues by using the previous calibration factor (see discussion of FDCbelow), or impedance (see discussion of EIS-based “smart calibrations”below), to predict if sensitivity has changed. Various embodiments alsouse time limits to maintain predictability for users, as well as includesteps (in the associated methodology) to ensure that detection is robustto variations between sensors.

FIG. 111 shows a flow diagram in accordance with an embodiment for FirstDay Calibration (FDC). Starting at block 9150, if FDC is not on aftersuccessful calibration, there is simply no smart calibration request(9151). However, if FDC is on, a determination is made at block 9153 asto whether this is the first calibration and, if it is not, then a smartcalibration request is made, with the timer set for 6 hours, i.e., it isrequested that an additional calibration be made in 6 hours (9155). If,on the other hand, this is the first calibration, then block 9157determines whether the Cal Ratio is less than 4, or greater than 7. Ifthe condition in block 9157 is not met, then the logic proceeds to block9155 where, as noted above, a smart calibration request is made, withthe timer set for 6 hours. However, if the criterion in block 9157 isnot met, then a smart calibration request is made, with the timer setfor 3 hours, i.e., it is requested that an additional calibration bemade in 3 hours (9159). Thus, in order to improve accuracy for sensorswhich need calibration adjusted, additional (smart) calibrations arerequested which, in turn, limit the amount of time where the adjustmentis incorrect.

In contrast with FDC mode, EIS-based smart calibration mode provides foradditional calibrations if impedance changes. Thus, in one embodimentshown in FIG. 112, an allowed range relating to impedance values (and asdefined hereinbelow) is set in the hour after calibration and, followingthe calibration, a request for additional calibrations is made ifimpedance is outside of range. Thus, if not within one hour sincecalibration, a determination is made as to whether the filtered 1 kHzimaginary impedance value is outside of range (9160, 9162). If theimpedance value is not outside of range, then no change is made (9164).However, if the filtered 1 kHz imaginary impedance value is outside ofrange, then the calibration timer is updated so that calibration isrequested to be performed at 6 hours from the previous calibration(9168). It is noted that, while higher-frequency imaginary impedancetends to better identify changes in glucose sensitivity, towards thehigher end of the frequency spectrum, measurements are generally noisierand, as such, may require filtering.

Returning to block 9160, if it is determined that less than one hour haspassed since calibration, then the range for impedance values may beupdated (9166). Specifically, in one embodiment, the impedance rangecalculation is performed on the last EIS measurement 1 hour aftercalibration. In a preferred embodiment, the range is defined as

range=3×median(|x _(i) −x _(j)|)

where j is the current measurement, and i are the most recent 2 hours ofvalues. In addition, the range may be limited to be values between 50Ωand 100Ω. It is noted that the range as defined above allows for 3 timesmedian value. The latter has been discovered to be more robust than the2-standard-deviation approach used in some prior algorithms, whichallowed noise and outliers to cause inconsistencies.

Embodiments of the invention for continuous glucose monitoring (CGM) arealso directed to using Kalman filters for sensor calibration,independently of the actual design of the subject sensor(s). As notedpreviously, sensor calibration generally involves determination of a CalFactor (CF) based on a reference blood glucose (BG), the associatedIsig, and an offset value. The BG and Isig, in turn, may include noise,and the offset may be sensor (design)-specific, such that the Cal Factoris also sensor-specific. However, by utilizing an Unscented Kalmanfilter, an underlying calibration methodology may be developed that issensor-unspecific, so long as the sensor is linear. Thus, a singlecalibration methodology (and related systems) may be used to calibratevarious sensors, without the need to re-calculate a calibration factorand/or an offset value for each specific sensor, and without the need todesign a (separate) filtering mechanism to compensate for noise. In thisway, both Cal Factor and offset can be allowed to change over timewithout the need to change the codebase on which the calibrationalgorithm otherwise operates.

In this regard, it is known that, every time a new glucose sensor isdeveloped, there is a need to re-evaluate and re-generate themethods/algorithms used for calibration. As part of such re-evaluation,assumptions, as well as constants, must be re-defined for each newsensor design. In addition, the mathematics in the calibrationmethodology is, in general, heuristically (and manually) reviewed. As isdescribed in detail hereinbelow, however, use of the unscented Kalmanfilter provides for a calibration methodology, wherein the onlyassumption is that the sensor is linear (although other, includingnon-linear, relationships may also be accommodated by modified versionsof the instant inventions). This, in turn, provides a significantadvantage, as the invented methodologies can be applied to any newlinear sensor, thereby significantly reducing development times for newsensors.

In existing methodologies, where the relationship between Isig and BG isgenerally assumed to be linear, the calibration factor (for a singleworking electrode, WE) may be calculated as

CF=BG/(Isig+offset)

Given that, typically, there is noise in the reference BG as well as inthe Isig, some filtering may be applied so that several BGs can beaveraged over time, and/or using complex functions of BG level, therebyproviding more robust calibration. The sensor glucose value (SG) maythen be calculated as

SG=CF×(Isig+offset)

More specifically, as has been noted, a periodic sensor measurement (SG)may be represented by the following relation

SG=CF(Isig+offset)+ε_(s)

where “Isig” denotes the physical output of the sensor (current in nA),and “CF” represents the calibration factor that relates the glucoselevel to the measured output. The calibration factor is not knownprecisely and varies over time; as such, it is estimated and compensatedin real time. The sensor bias is represented by “offset”, which is atime variant variable, and random sensor error is represented by ε_(s).The latter is completely random and, as such, cannot be estimated.

Blood glucose (BG) level is measured using the finger stick, e.g., via ameter. A general BG measurement differs from SG by a random error(ε_(B)), i.e.,

SG=BG+ε _(B)

There is also a first order lag between sensor glucose measurements (SG)and physical output (Isig). Thus,

$\overset{.}{SG} = {{{- \frac{1}{\tau}}{SG}} + {\frac{1}{\tau}({Isig})}}$

where τ is time constant that defines the dynamic relationship betweenSG and Isig. In the above relationship, τ is not known precisely, andcan vary by patient, sensor location, time, and and/or other variables.Assuming that the time constant is constant (e.g., ⅙ h=10 min), adynamic variable may be established which can be treated as an uncertainparameter that is then estimated and compensated using a Kalman filter.

Generally speaking, a Kalman filter is an optimal estimator that uses aseries of measurements containing noise and produces statisticallyoptimal estimates of unknown variables. It is recursive, such that newmeasurements can be processed as they arrive to update the estimates.While Kalman filters, in general, require linearization ordiscretization of the underlying equations that describe the state ofthe system being evaluated, an Unscented Kalman Filter deals directlywith any such nonlinearity in the measurement equation.

Nonlinear Dynamic Process Model

Three variables that may be used for the above-mentioned estimation aresensor glucose (SG), calibration factor (CF), and offset. Themeasurement is blood glucose (BG), which, as noted above, is related tosensor current (Isig). Based on the aforementioned variables, thefollowing states may be defined:

-   -   x₁=SG    -   x₂=CF    -   x₃=Offset    -   U=Isig        Using the prior equations relating BG, SG, CF, and the first        order lag, the following is then derived:

$\quad\left\{ \begin{matrix}{{{\overset{.}{x}}_{1}(t)} = {{{- \frac{1}{\tau}}{x_{1}(t)}} + {\frac{1}{\tau}{u(t)}}}} & \; \\{{{\overset{.}{x}}_{2} = {{{x_{2}(t)}t} < T_{d}}};{{ax}_{2}(t)}} & {t \geq T_{d}} \\{{\overset{.}{x}}_{3} = {x_{3}(t)}} & \;\end{matrix} \right.$

where α=0.995, τ=⅙ h=10 min, and u(t)=Isig. As has been noted previouslyin the instant specification and description, sensor response istypically different at the beginning (e.g., first day) of sensor lifethan the remainder of the sensor's life. Therefore, in the instantanalysis, it is also assumed that the sensor response at the beginningis different from the rest of its lifetime. Thus, in the aboverelationship, T_(d) is defined for the first day.

Using the above state variable definitions, the SG measurement, which isan estimation of BG using the finger stick, becomes:

z(t)=x ₂(t)(u(t)+x ₃(t))+v ₁

where z=BG, and u(t) is the first Isig measurement after BG measurement.The sensor glucose is the estimation of blood glucose, i.e.,SG={circumflex over (B)}G. Because the BG measurements are provided insampled form, no discretization is needed in order to implement thediscrete time measurement in the above equation.

In order to apply an Unscented Kalman filter to continuous glucosemonitoring, the above equations for {dot over (x)}(t) and z(t) must bepresented in a nonlinear format, i.e.:

$\quad\left\{ \begin{matrix}{{\overset{.}{x}(t)} = {{f\left( {{x(t)},{u(t)},t} \right)} + {w(t)}}} \\{{z(t)} = {{h\left( {{x(t)},{u(t)},t} \right)} + {v(t)}}}\end{matrix} \right.$

where u is the input, w is the state noise, z is the measurement vector,and v is the measurement noise. It is noted that, while both v and w areassumed to be uncorrelated zero-mean Gaussian white noise sequences,they can be modified depending on statistics that may be captured fromdata. Unlike the Kalman and Extended Kalman filters, the UnscentedKalman filter does not require linearization or discretization of theequations. Rather, it uses a true nonlinear model and approximates thedistribution of the state random variable. Thus, while the goal is stillto compute the Cal Factor, the complexity in the latter computation iscontained within the underlying model and methodology described herein.In other words, within the context of glucose-sensor calibration andoperation, the calibration is performed through the Unscented Kalmanfiltering framework. In this regard, as noted, the (Unscented) Kalmanfilter includes robustness against noise in the calibration by assumingexistence of a noise distribution in both the BG (i.e., the measurementnoise v) and the Isig (i.e., the state noise w), and compensating forsuch noise implicitly in the algorithm. Thus, the unscented Kalmanfilter enables real-time calibration that estimates both Cal Factor andoffset, accounting for changes over time.

Initial Conditions and Covariance Matrix

For the above-described framework, state vector initialization andcovariance are given as:

${\hat{x}(0)} = \begin{bmatrix}{{BG}(0)} \\4 \\{- 4}\end{bmatrix}$ ${P(0)} = \begin{bmatrix}15 & 0 & 0 \\0 & 0.1 & 0 \\0 & 0 & 0.1\end{bmatrix}^{2}$

The diagonal elements of process noise covariance matrix, Q, shownbelow, are variances that represent the uncertainties in the knowledgeof each state that accumulate between measurements.

$Q = \left\{ \begin{matrix}\begin{bmatrix}5 & 0 & 0 \\0 & 0.2 & 0 \\0 & 0 & 0.1\end{bmatrix}^{2} & {t < T_{d}} \\\begin{bmatrix}5 & 0 & 0 \\0 & 0.1 & 0 \\0 & 0 & 0.1\end{bmatrix}^{2} & {t \geq T_{d}}\end{matrix} \right.$

These values should be based upon observations of the unpredictablevariations of these processes when scaled over the measurement time, t.The measurement error variance, R, is equal to 3% of the BG measurementvalue, squared. Thus,

R=0.03×z(t)

With the above structure and methodology, BG measurements are runthrough an Unscented Kalman filter, and the calibration factor isestimated. The calibration factor, in turn, is used to transform Isig toSG, as discussed previously.

FIG. 113 shows a block diagram of an existing calibration process for asingle working electrode. Using the Isig from the working electrode (WEIsig), a pre-processing step 9210 is first performed that may, e.g.,include filtering, averaging, and/or weighting of several Isig valuesfor the single WE to generate a single optimized Isig value. The latteris then calibrated 9220 using the offset and a calibration BG 9230, suchas, e.g., a finger stick meter measurement, to calculate a calibrationfactor CF which, in turn, is used to calculate a sensor glucose valueSG. Post processing 9240 is then performed on the SG to generate a morerobust and reliable sensor glucose value SG.

FIG. 114 shows a block diagram for calibrating a single workingelectrode sensor using a Kalman filter. As before, Isig from the workingelectrode (WE Isig) is the input into a pre-processing step 9212, wherea plurality of Isig values may be, e.g., filtered, averaged, and/orweighted to generate a single optimized Isig value. A calibration BG9232 is then used to calculate a CF and SG in step 9222. However, now,step 9222 is carried out using an unscented Kalman filter, such that thecalculation of the actual calibration factor and the resultant sensorglucose value is carried out through the Kalman filter, using themethodology and relationships described hereinabove. In step 9242, thecalculated SG is subjected to post-processing to generate a more robustand reliable sensor glucose value SG. In an alternative embodiment shownin FIG. 115, the Kalman filter may be used to perform the pre-processingfunctions in addition to the calibration and SG calculation (9217).

Multi-Electrode System and Fusion

In a further embodiment, a Kalman filter may be used to calibrate amulti-electrode system. Specifically, as shown in FIG. 116, a systemwith N working electrodes may have the respective Isig from eachelectrode pre-processed 9214, 9216, 9218, as described hereinabove. Asshown in blocks 9224, 9226, 9228, the processed Isig from each workingelectrode may then be calibrated, and a respective SG calculated, usingan unscented Kalman filter and a calibration BG 9234. The respective SGsfrom each of the N working electrodes may then be fused andpost-processed in block 9244, resulting in a final, fused SG.

It is noted that, while, in the above description, the Kalman filter isapplied in the calibration step only, in alternative embodiments, theKalman filter may be used in one or more of the pre-processing step9214, 9216, 9218, the calibration and SG calculation step 9224, 9226,9228, and/or the SG fusion and/or post-processing step(s) 9244. Inaddition, as shown in FIG. 117, a single Kalman filter can be used tocalibrate all working electrodes together, e.g., by including allelectrodes in the same Kalman filter state space equation. Moreover, thefusion step may be carried out by using the generalized Millman formulaand/or one of the fusion algorithms that were discussed previously inthis specification in connection with fusion of multiple Isig ormultiple SG values (including, e.g., weighting of individual Isig and/orSG values). Thus, the unscented Kalman filter may be used, e.g., inconjunction with EIS data to optimize SG (or Isig) fusion inmultiple-electrode systems.

It is also important to note that, as part of the fusion methodology,the post-processing step which was described previously may include apredictive component, whereby physiological delays between blood glucoseand interstitial glucose may be accounted for. Here, past values ofsensor glucose SG are used to predict a (future) value for SG, with theamount of prediction to be applied at each time step depending on thelevel of noise in the system. FIG. 118 is a table comparing the resultsof applying a current fusion algorithm (“4D Algorithm”), on the onehand, and an unscented Kalman filter, on the other, to various sensordata sets. As shown in FIG. 118, in each instance, application of theKalman filter provided notable improvements in the Mean AbsoluteRelative Difference (MARD) while, at the same, allowing a single Kalmanfilter model to be applied across all of the datasets, even though thereare significant design differences amongst the sensors for which thedatasets were gathered. Thus, e.g., whereas application of the 4DAlgorithm to the Australia dataset resulted in a fusion MARD of 9.72,use of the unscented Kalman filter with the same dataset provided a MARDof 9.66.

As discussed previously in connection with FIGS. 33-35 and 116, fusionalgorithms may be used to generate more reliable sensor glucose values.Specifically, fusion algorithms fuse independent sensor glucose valuesto provide a single, optimal glucose value to the user. Optimalperformance, in turn, may be defined by accuracy, duration and rate ofdata availability, and minimization of fault states that could burdenthe user. As before, it is noted that, while the ensuing discussion maydescribe aspects of a fusion algorithm in terms of a first workingelectrode (WE1) and a second working electrode (WE2) as redundantelectrodes, this is by way of illustration, and not limitation, as thealgorithms and their underlying principles described herein areapplicable to, and may be used in, redundant sensor systems having morethan 2 working electrodes. In addition, such redundancy may be simple,orthogonal, pseudo-orthogonal and/or complex.

In an embodiment of the inventions herein, a SG fusion algorithm isdriven by a number of inputs, such as, e.g., Electrochemical ImpedanceSpectroscopy (EIS), noise, and calibrations. These inputs dictate howthe algorithm combines independent electrode sensor glucose values toprovide the final fused sensor glucose value, as well as the logicgoverning calibration, data display, and user prompts. Specifically, thefusion algorithm calculates weights for each individual sensor glucosevalue (i.e., the glucose value from each of the working electrodes). Thesum of the weights must total 1. In other words, the fusion glucosevalue is a weighted average of the individual sensor glucose values, asdefined by the relation:

${FG} = {\sum\limits_{k = 1}^{N}{{SG}_{k}*{FW}_{k}}}$

where, at a given time, FG is Fusion Glucose, SG_(k) is the sensorglucose value of the k^(th) working electrode, and FW_(k) is the finalfusion weight assigned to the k^(th) SG value for a system with Nworking electrodes.

The weights, to be explored further hereinbelow, are derived viatransformation of a series of fusion inputs, including noise, EIS-basedsensor membrane resistance (Rmem), and calibration factor (Cal Factor,or CF). As has been discussed previously, noise and Rmem are endogenousinputs, driven by the sensor without any explicit input from the user.In this regard, the fusion algorithm will generally favor electrodeswith lower noise and lower membrane resistance. Cal Factor, on the otherhand, is a ratio between the calibration blood glucose values and theraw sensor current value (Isig), and, as such, is derived from userinput. Here, the fusion algorithm will favor electrodes with calibrationfactors that fall within a range defined as optimal. With the “favoredelectrodes” thus defined with respect to noise, Rmem, and Cal Factor,the fusion algorithm then weighs the more-favored electrode(s) moreheavily in the final fused glucose calculation. As shown in FIG. 119,each type of input calculates a set of values that distribute the weightin a ranked fashion, and each type of weight is combined to calculatethe final raw fusion weight.

The fusion inputs are transformed via a series of functions to produce aset of weights. A ratioScore function calculates the raw fusion weightacross a collection of electrodes for a given input (e.g., noise) and,in one embodiment, may be expressed as:

$r_{k} = {\frac{1}{N - 1}\left( {1 - \frac{\epsilon_{k}}{\sum_{n = 1}^{N}\epsilon_{n}}} \right)}$

This function, or equation, is appropriate for inputs where lower valuesindicate better performance, (e.g., noise and membrane resistance), andtherefore will receive greater fusion weight. Thus, for example, noisefrom all electrodes at a given time is passed to the ratioScorefunction, which assigns to each electrode a score (also referred to asweight or ratio) that is inversely proportional to the amount of itsnoise relative to the sum of noise across all electrodes. In the aboveequation, therefore, the raw noise fusion weight (ratio) at a given time(r_(k)), for working electrode k, is expressed as a function of thenoise on working electrode k (ε_(k)) for a system with N>1 workingelectrodes.

In particular, the first argument in the above ratioScore functionnormalizes the value inside the parentheses so that the sum of r_(k)across all working electrodes totals 1. The second argument inside theparentheses is a ratio of the noise of the individual k^(th) workingelectrode to the sum of noise values across all working electrodes(sigma operator). The ratio is then subtracted from 1 so that anelectrode with low noise receives a high value.

As noted, the above equation applies to inputs for which lower valuesindicate better performance. For inputs where greater values indicatebetter performance, a simpler equation calculates the raw fusion weight.Specifically, the following ratioScore function is used to simplynormalize the given metric δ by the sum across all working electrodes:

$r_{k} = \frac{\delta_{k}}{\sum_{n = 1}^{N}\delta_{n}}$

In the foregoing equation, the input on working electrode k is given byδ_(k) for a system with N>1 working electrodes.

The raw fusion weight scores (or ratios)—as calculated using one of thetwo equations above—are then passed to a ratioGain function, whichemphasizes or deemphasizes the relative scores based on a pre-definedparameter. While raw ratioScore values provide appropriate weighting interms of ranking, they do not necessarily distribute the weights in anoptimal manner. As such, an equation is defined which exaggerates ordeemphasizes the distribution of weight ratios based on a “gain factor”parameter. Thus, in an embodiment of the inventions herein, the gainedratio weight, g, is defined as follows:

$g = {{\frac{1}{N}\left( {1 - m} \right)} + {m*r}}$

where r is the raw fusion weight ratio, and m is the “gain factor”parameter for a system with N>1 working electrodes. The output g maythen be saturated to the range [0,1] such that, if the output is greaterthan 1, then the output is set to 1, and if the output is less thanzero, then the output is set to 0. In this regard, a saturation functionthat may be used in conjunction with embodiments of the invention may bedefined as:

${f(x)} = \left\{ \begin{matrix}{a,} & {x < a} \\{x,} & {a \leq x \leq b} \\{b,} & {x > b}\end{matrix} \right.$

It is noted that, in embodiments of the inventions herein, a sigmoidalor otherwise smooth function may also achieve similar results as above.

Finally the values are processed through the makeSumOne function toensure that the sum totals 1, and to normalize if necessary. Thus,individual values divided by the sum of all values yield relativeratios, with the makeSumOne function defined as follows:

$s_{k} = \frac{g_{k}}{\sum_{n = 1}^{N}g_{n}}$

Diagrammatically, the algorithm discussed hereinabove may be shown fornoise, and Rmem weights, respectively, as follows:

As can be seen from the above diagrams, the calculation of a set ofnoise weights from all individual noise weights follows the same generalalgorithm as that for computing a set of Rmem weights from allindividual Rmem inputs.

In embodiments of the invention, Cal Factor weighting is calculated in asimilar fashion, but with an additional step, involving acalFactorTransform function, as shown below:

Calibration factor values from all electrodes at a given time are firstpassed to the calFactorTransform function. Specifically, the calibrationfactor is transformed to a score via the following function for anormalized log-normal curve:

${f(x)} = {\frac{1}{2\sigma^{2}}*\frac{e^{{({{{- \ln}\; x} - \mu})}^{2}}}{x*e^{({{0.5\sigma^{2}} - \mu})}}}$

where x is the raw (input) calibration factor, f(x) is the transformed(output) Cal Factor, and parameters σ and μ describe the width and peakof the log-normal curve, respectively.

Next, the results are saturated to the range [0.001, clip], where alltransformed scores greater than the parameter clip will be assignedequal score. Here, higher scores will receive greater weight and, assuch, the second of the two ratioScore functions note above

$\left( {{i.e.},{r_{k} = \frac{\delta_{k}}{\sum_{n = 1}^{N}\delta_{n}}}} \right)$

is used. As shown, the rest of the algorithm follows the proceduredescribed previously for noise and Rmem.

Returning to FIG. 119, the flow diagram of FIG. 119 shows how each setof the weights is combined to calculate the final raw fusion weight.Specifically, the raw Fusion Weight is calculated by weighting andaveraging the noise (9302) and Cal Factor (9304) weights by thenoiseBalance parameter (9308). The combined noise and Cal Factor weightis then weighted and averaged with Rmem weight (9306) by the RmemBalancevariable (9310). For purposes of the forgoing, the parameternoiseBalance (9308) is predefined to specify the balance between noise(9302) and Cal Factor (9304) weights. In a preferred embodiment of theinvention, noiseBalance may be a constant having a value of 0.524.

In addition, the variable RmemBalance (9310) is determined as follows(see also discussion below in connection with FIG. 120): From the time asensor starts, after a pre-defined duration, RmemBalance is set to zero.In other words, after a pre-defined time from sensor start,rawFusionWeight (9318) receives zero contribution from Rmem. Prior tothe pre-defined time—i.e., from the time a sensor starts up until thepre-defined duration—on the other hand, RmemBalance (9310) is calculatedas shown and described below:

First, the min and max Rmem_Weights across all electrodes are selected.Then, the min is subtracted from the max, added to 1, and the totaldivided by 2; this operation approximates the variance in weights. Thisvalue is then passed to the TukeyWindow function (described below) whoseoutput is finally subtracted from 1. The purpose of these steps is tocalculate RmemBalance (9310) such that Rmem weight has a greateremphasis on fusion weights when there is a greater variation amongstRmem values.

The TukeyPlus defines a flat-top tapered cosine (Tukey) window where theparameter r defines the ratio of taper over the interval [0,1]. Thenominal tukeyWindow function is described below. Modifications can beimplemented to increase the taper rate by either introducing anadditional “frequency” parameter in front of the 2× arguments orexponentiating the entire piecewise function:

${f(x)} = \left\{ \begin{matrix}{{\frac{1}{2}\left\lbrack {1 + {\cos \left( {\frac{2\pi}{r}\left\{ {x - \frac{r}{2}} \right\}} \right)}} \right\rbrack},} & {0 \leq x < \frac{r}{2}} \\{1,} & {\frac{r}{2} \leq x < {1 - \frac{r}{2}}} \\{{\frac{1}{2}\left\lbrack {1 + {\cos \left( {\frac{2\pi}{r}\left\{ {x - 1 + \frac{r}{2}} \right\}} \right)}} \right\rbrack},} & {{1 - \frac{r}{2}} \leq x \leq 1}\end{matrix} \right.$

With the above in mind, a detailed description of the SG fusionalgorithm in accordance with embodiments of the inventions herein willnow be provided. FIG. 120 shows the general outline of the fusionalgorithm, which takes as input (9350) respective sensor glucose values(SGs) that have been calculated for individual sensors (i.e., individualworking electrodes). It is reiterated that, by way of illustration andnot limitation, FIG. 120 describes the fusion process with reference totwo working electrodes, each of which generates a respective SG (i.e.,SG1 and SG2). The algorithm, however, may be applied to a larger numberof working electrodes.

At block 9352, a determination is made as to whether any of the SGs isinvalid. If both SGs are determined to be invalid (9354), the overallfusion is set to “invalid” (9356). However, if only one of the SGs isinvalid (9358), then the other (valid) SG is set as the Fusion SG (9360,9362). If, on the other hand, all SGs are valid, the next step in theprocess 9370 determines whether the “FUSION_START_TIME_SWITCH” has beenreached. As explained previously in connection with FIG. 119, inembodiments of the inventions herein, this is a pre-defined durationsince sensor start, after which RmemBalance is set to zero. In apreferred embodiment, the pre-defined duration (after sensor connection)after which the fusion algorithm switches from Rmem logic to Cal Factorand Noise logic is about 25 hours.

Thus, if the current time is after the “FUSION_START_TIME_SWITCH”, thenRmem-based fusion is disabled, such that Rmem makes no contribution tothe final fusion weight (9380). If, on the other hand, the current timeis before “FUSION_START_TIME_SWITCH”, then Rmem-based fusion is enabled(9372), such that Rmem fusion weights are calculated as describedhereinabove, and the relative contribution of Rmem fusion weight tofinal fusion weight is calculated based on the magnitude of Rmemdifferences (9374).

Regardless of whether Rmem-based fusion is disabled (9380) or enabled(9372, 9374), the algorithm next provides for calculation of Cal Factorand Noise fusion weights in block 9376. The combined Cal Factor andNoise (CCFN) and Rmem fusion weights are then combined, final fusionweights are calculated and values are smoothed (9377). Finally, as shownin block 9378, SG_Fusion is calculated as ri_1*SG1+ri_2*SG2 (for atwo-working-electrode system), where ri_1 and ri_2 are the variablesthat are used to compute fusion weighting.

In connection with the fusion algorithm described herein, the behaviorof each constituent working electrode, which behavior may then beduplicated prior to fusion, may be described as follows in connectionwith a preferred embodiment:

First Stage Filtering: Conversion of 1 Minute to 5 Minute Values

For each individual working electrode (WE), the algorithm uses the mostrecent 8 minutes of sensor current data to create a five minute Isig.This is referred to as the first stage filtering. The algorithm usesinformation from the system to identify periods in which the sensor datahas been impacted by the diagnostic module. The algorithm then modifiesthe raw sensor signal (1 minute sensor current) by replacing packets inwhich gross noise and/or diagnostic interference is detected.

The algorithm computes (1) discard and (2) five minute Isig byapplication of a simple 7th order FIR filter on the one minute data,using the following coefficients for the filter: [0.0660; 0.2095;0.0847; 0.1398; 0.1398; 0.0847; 0.2095; 0.0660]. The discard flag willbe true or false based on the variability in 1 minute sensor currentmeasurements over the most recent 8 measurements (8 minutes). Thediscard flag will be false when there are fewer than 4 measurementsfollowing a sensor connection. On the other hand, the discard flag willbe true if 4 or more measurements in the buffer fail the followingconditions: (a) 1-minute sensor current is less than 1 nA; (b) 1-minutesensor current is greater than 200 nA; (c) 1-minute sensor current isless than AverageCount×2 with two decimal place precision; (d) 1-minsensor current is greater than AverageCount×2. Here, “AverageCount” isthe average of the middle 4 values if the FIR history has 8measurements; otherwise, it is taken as the average of the existingmeasurements in the FIR history. It is noted that, in a preferredembodiment, the discard-flag-true event will only trigger if the bufferhas 5 or more measurements.

Identification of Invalid Packets

For every 5 minute packet, the signal will be checked to verify if thepacket is valid. If any of the following criteria are met, the packetwill be considered invalid: (a) the 5-minute Isig value is aboveMAX_ISIG or is below MIN_ISIG; (b) the Vcntr is above 0 Volts or lessthan −1.3 Volts; (c) the packet is flagged as an artifact; (d) thepacket was flagged as discard when converting the 1 minute data into the5 minute Isig; (e) 1 kHz Real Impedance is out of range; and (f) Highnoise (see Noise Check section discussed hereinbelow). In a preferredembodiment of the invention, MAX_ISIG and MIN_ISIG, the thresholds usedto identify invalid Isigs, are 200 nA and 6 nA, respectively.

Artifact Detection

On every 5-minute packet, artifact detection may be performed toidentify large and small drops in Isig to prevent the data from beingused in SG calculations. For large drops in Isig, the event may beclassified as a “big artifact”, for which all subsequent packets areflagged as discard and will be considered part of an artifact eventuntil termination conditions are met. Smaller drops, which may beclassified as “small artifacts”, only allow that single packet to beflagged as discard; the following packet can only be flagged as discardby this artifact detection algorithm if it is detected to be a bigartifact. If the packet is flagged as “init” (i.e., initialization, withthe data referring to data during the sensor warm-up period), theartifact detection variables are set to default values and no artifactsare detected.

For every 5-minute packet that is not an initialization packet, twovariables nA_diff_(i) and pct_diff_(i), are defined as follows:

nA_diff_(i)=isig_(i)−isig_(i-1)

pct_diff_(i)=100×(nA_diff_(i)/isig_(i-1))

where isig_(i) represents the value in nA of the ith Isig, andisig_(i-1) is the previous Isig. If the previous packet was not a smallartifact and not a big artifact state, the current packet may be flaggedas a discard if pct_diff_(i)<−25 and nA_diff_(i)<−4.

Identifying Start of Big Artifact

If the previous packet was not a big artifact, the current packet willbe flagged as discard and considered the start of a big artifact if anyof the 3 conditions below are true:

pct_diff_(i)<−40 AND nA_diff_(i)<−5

pct_diff_(i) +pct_diff_(i-1)<−50 AND nA_diff_(i)+nA_diff_(i-1)<−13

pct_diff_(i) +pct_diff_(i-1) +pct_diff_(i-2)<−60 ANDnA_diff_(i)+nA_diff_(i-1)+nA_diff_(i-2)<−18

After Detection of a Big Artifact

For every packet in the big artifact state, including the packetdetecting the artifact, the packet flagged as discard. Once detected asan artifact, the state of an artifact is determined on each packet. Inthis regard, valid states are: (1) Falling; (2) Nadir Stability; and (3)Rising. Exit from the big artifact state can occur if any of thefollowing 4 conditions is met: (1) Isig is high and stable after beingin the Rising State; (2) Previous state was Rising, Isig is stable, andsystem has been in the Rising state for several packets; (3) The systemhas been in the artifact state for a prolonged period, the maximumlength being defined upon detection of the artifact; and (4) There is adisconnect.

Small Dropout Detection

The dropout structure is updated every packet and indicates if thecurrent packet is in a dropout, and has associated variables so thefilter can account for the dropout. The overall logic is as follows: Adropout state is detected as any of the following three generalconditions: (1) A rapid drop: A rapidly decreasing Isig, while previouspackets showed a more stable signal; (2) A directional change: Amoderately fast decreasing Isig with previous packets having low noiseand an increasing Isig; (3) A moderate drop: Isig decreasing at amoderate level with previous packets showing very low noise. Once any ofthese events is detected, the measured decrease in Isig is added back tothe raw Isig prior to filtering, and the Isig threshold to exit thedropout state is defined. The logic exits from the dropout state if thisstate persists for too long or the Isig increases sufficiently.

Noise Estimate

Next, noise_level and freq_equiv are determined for the current packet,which are then used in the filtering section. The noise_level isadditionally used in identifying dropouts and identifying a sensor endcondition (see section on NoiseCheck). This process requires the twomost-recent values for noise_level. Specifically, noise_level iscalculated based on the absolute value of the seven (7) most-recentsecond derivative of Isig (isig_acc) values, scaled by 9×calFactor, andclipped to be between 0 to 10. In a preferred embodiment, a defaultnoise_level may be set of 7.5 if the current or prior second derivativecalculation was not performed. The variable freq_equiv is calculated asfollows, using the five (5) most-recent unfiltered Isig rate of changevalues:

Freq_equiv=abs(mean(roc))*calFactor

where “roc” is the rate of change in nA/min. After the abovecalculation, the freq_equiv value is then clipped to 0.2 to 4 mg/dL/min.If three or more isig_acc values are invalid, or the noise_levelcalculated is over 7, then freq_equiv is set to a default value of 0.9.

Rates of Change (ROC) Estimate

The first and second derivatives of Isig are used to estimate noise,identify dropouts in the signal, compensate for delay, and reduce thefalse errors when performing the instant calibration error check. Bothfiltered and unfiltered rates of change are calculated. In connectionwith the former, a Savitzky-Golay smoothed rate of change is calculatedusing the 5 most-recent Isig values, and replacing any invalid Isigswith the most-recent valid Isig. Thus:

Weights=[0.2;0.1;0;−0.1;−0.2];% same as coeff/Norm: [2;1;0;−1;−2]/10

roc_savitisig=sum(rawisig.*weights)/time_since_last_packet;% unitsnA/min

The unfiltered Isig rate of change (variable roc_rawisig) is calculatedby subtracting the prior Isig from the current Isig, and dividing by thetime difference (5 minutes). The second derivative of the unfilteredIsig (acc_rawisig) is calculated by subtracting the (first derivative)roc_rawisig value calculated with the prior packet from the currentpacket and dividing by the time difference, as follows:

acc_rawisig=(roc_rawisig(1)−roc_rawisig(2))/5

Isig Filtering

The calculations that are used to determine fIsig, the filtered Isigvalue used for calibration and calculating SG, will now be described.The filter parameter “q” adapts based on the noise_level and freq_equiv,so that under low noise or high rates of change, fIsig will be close tothe unfiltered value. When Isig data is invalid, the filter outputremains unchanged from the previous output. The filter will be reset atSENSOR_WARMUP_TIME, which is defined as the time after sensor connectionwhen SGs may begin to be displayed to the user. In preferred embodiment,SENSOR_WARMUP_TIME is about one hour.

If the resulting fIsig is an unexpected value, specifically above 202.5nA or under 3.5 nA, a Change Sensor alert is issued. If the resultingfIsig is greater than or equal to 3.5 nA and less than MIN_ISIG, then itwill be clipped at MIN_ISIG. As noted previously, in preferredembodiments of the invention, MIN_ISIG may be set at 6 nA. However, ifthe resulting fIsig is less than or equal to 202.5 nA and greater thanMAX_ISIG, then it will be clipped at MAX_ISIG. As has been describedpreviously, in preferred embodiments of the invention, MAX_ISIG may beset at 200 nA.

Isig Delay Compensation

Employing a Kalman filter, a predicted Isig is used as the measurementinput. The prediction, in turn, is calculated based on the Isig rate ofchange, clipped to prevent adding excessive prediction. The amount ofprediction added is regulated by the presence of invalid data and noise(from noise_level) calculation.

Kalman_state Calculations

The kalman_state.q value (used in the ensuing equations) is calculatedusing the noise_level and freq_equiv values described in the NoiseEstimate section. If the system is in a dropout, roc is not added toIsig. Instead, the dropout amount is added, and the kalman_state.qcalculated is modified to provide more filtering. The followingcalculations are used to determine the values to store forkalman_state.x and kalman_state.p. The value for cur_isig includes thedelay compensation added to the five minute Isig.

Kalman_state.p=kalman_state.p+kalman_state.q

kalman_state.k=kalman_state.p/(kalman_state.p+kalman_state.r)

kalman_state.x=kalman_state.x+kalman_state.k*(cur_isig−kalman_state.x)

kalman_state.p=(1−kalman_state.k)*kalman_state.p

EIS Events

Every time an EIS event is triggered, measurements are taken on thefollowing frequencies (in Hz), with the sequence being repeated per WE:[0.105, 0.172, 0.25, 0.4, 0.667, 1, 1.6, 2.5, 4, 6.3, 10, 16, 25, 40,64, 128, 256, 512, 1024, 2048, 4096, 8192]. If one of the EISmeasurements is flagged as saturated or discard, the entire set ofmeasurements per WE will not be used.

Blood Glucose (BG) Entry

As has been noted, the calibration ratio (CR), which is used for thecalibration error checks, may be calculated as follows:

CR=BG/(fisig+offset)

Only BG entries greater than or equal to 40 mg/dL and less than or equalto 400 mg/dL are used for calibration, and values outside this rangewill be rejected. If no new sensor command or old sensor command hasbeen received, or the most recent packet was flagged as “init”, the BGwill be rejected. If no packet exists prior to the BG entry (such asafter a new sensor command), the BG entry will be rejected. The BG entrywill be rejected if the timestamp indicates it is too old or in thefuture.

Instant Calibration Error Check

If a BG is not rejected by the basic checks, it will be checked for acalibration error using the most recent fIsig from both WEs value. In apreferred embodiment, this is the only place where a calibration errorwill be issued. If there is a calibration error on both WEs, a new,successful BG entry will be required to continue showing SG value, andthe BG which caused the calibration error will not be used forcalibration. The following conditions are considered single WEcalibration errors: (a) The previous packet has an invalid Isig; (b) TheCR is outside the calibration error thresholds; (c) The CR is different,e.g., beyond a threshold, from both the previous CR and the currentcalFactor; (d) Larger thresholds are used if the system expects highererror, specifically in the FDC adjustment, IsigDip adjustment mode, orthe estimated rate of change exceeds 1.5 mg/dL/min. In preferredembodiments, calibration error thresholds may be set as follows: 40mg/dL for a smaller threshold used for typical CE checks (THRESH_MGDL),and 50 mg/dL for a larger threshold (THRESH_MGDL_LARGE), used whenlarger errors are expected during CE checks.

When a BG entry does not cause a calibration error, the single WEcalibration error counter will be set to 0, and the BG will be used toupdate the calFactor. If the algorithm identifies a BG as causing asingle WE calibration error, but a BG is pending final calibration, theBG is rejected, and calibration continues, using the previously acceptedBG on that WE. If a new BG passes the calibration error checks, itreplaces any current BG values that are pending final calibration. Ifthe algorithm identifies a BG as causing a calibration error not due toan invalid Isig, and the above does not apply, then: (1) if thecalibration error counter is 1, and less than 5 minutes have elapsedsince the transmitter identified the previous calibration error, the BGwithout incrementing the calibration error counter, thereby preventing achange sensor alarm from occurring from the same BG and fisig whichpreviously caused a calibration error; and (2) otherwise, thecalibration error counter is increased. If the counter was 0, then a newBG error is required to continue showing SG. Once the calibration errorcounter reaches 2 on a single WE, the WE is terminated, as SG can nolonger be calculated.

Embodiments of the inventions herein include a dynamic maximum CR limit.Specifically, the MAX_CR may be set at 16 at sensor startup, and reducedlinearly, as a function of time, to 12 over 4 days. The MAX_CR may befurther gradually reduced to 10 if the Vcntr value is high for aprolonged time. As has been described previously, a high Vcntr value istypically associated with high levels of noise in the Isig, as well assensitivity loss.

Working Electrode Calibration

As has been described herein, individual working electrodes willrequest/require calibration according to fixed intervals, or asdetermined in real-time by Smart Calibrations. In this regard, inembodiments of the inventions herein, the first successful calibrationmay expire in 6 hours, with subsequent calibrations expiring in 12hours. Smart Calibrations, based on EIS or First Day Calibration logic,may result in the expiration time being shorter, as discussed in theFirst Day Calibration and EIS sections.

In one preferred embodiment, the algorithm will continue to calculate SGfor an additional amount of time after standard calibration expiration(EXTRA_TIME), as well as after EIS Smart Calibration expiration(EXTRA_TIME_SMART). Accordingly, work electrode state is set to 1 ifcalFactor is expired, but within EXTRA_TIME or EXTRA_TIME_SMART, and setto 2 if calFactor is expired and after EXTRA_TIME or EXTRA_TIME_SMART.These SGs are stored in a separate SG buffer that does not affect thedisplay of SG. In embodiments of the invention, EXTRA_TIME is set to 12hours, and EXTRA_TIME_SMART is set to 6 hours.

Individual WE SG Calculation

The Cal Factor used to calculate SG is based on the most recentcalibration calculation or, if in an adjustment mode, the value updatedthrough the First Day Calibration Logic or Isig Dip Calibration Logic.The Cal Factor used to calculate SG must be less than MAX_CR and greaterthan MIN_CR. If the Cal Factor is outside of this range, the system willinvalidate the Cal Factor and set the working electrode state equal to2. Similarly, the filtered Isig used to calculate SG must be less thanMAX_ISIG and greater than MIN_ISIG. If the filtered Isig is outside ofthis range, the system will invalidate the Isig and set the workingelectrode state equal to 2. Working electrode state is set to 2 if CalFactor is expired or invalid, or the current packet is invalid.

BG to Isig Pairing

After a BG entry that did not cause a calibration error, the followingsteps are performed to update the Cal Factor. If the current packet isinvalid or the new BG would cause a calibration error, the Cal Factor isnot updated at this time. If the current packet is valid and the BGwould not cause a calibration error, a temporary update of thecalibration buffer is performed by adding the BG and current pairedsensor information to the calibration buffer and temporarily removingthe oldest paired information. The Cal Factor is then calculated asdescribed in the Cal Factor calculation section hereinbelow. If thereare previous calibrations, the calculated Cal Factor value must beweighted with respect to the previous Cal Factor. In one preferredembodiment, the weight is assigned as follows: 70% weight for new value,and 30% weight on old value. It is noted that, for a packet which occurs5 to 10 minutes after a successful BG entry, the calibration factor isupdated by selecting the most recent fIsig value which is closest to theprior calibration factor and does not cause a violation of thecalibration error criteria.

Calibration Buffer Update

In embodiments of the invention, the calibration buffer contains BGvalues, as well as the following paired information: the paired Isigvalue associated with each BG value in the buffer, the higher-frequencyimaginary impedance expected value, and the range expected impedancevalue. There are generally 4 positions in the calibration buffer, withposition 4 being the oldest entry. If the system is in Isig Dip Mode,and the CR is less than the most recent CR in the calibration buffer,then the calibration buffer is updated by replacing the most recententry (position 1) in the calibration buffer with the pending entryinstead of removing the oldest entry. If, however, the latter does notapply, the calibration buffer is updated by shifting the prior entries(removing the oldest entry at position 4), and putting the new pendingBG at position 1.

Cal Factor Calculation

If there is no calibration error, the Cal Factor may be updated inaccordance with the following relation, where Isig is the paired Isigvalue, and n is the number of valid entries in the calibration buffer:

${{Cal}\mspace{14mu} {Factor}} = \frac{\sum_{i = 1}^{n}{\alpha_{i} \times \beta_{i} \times \left( {{isig}_{i} + {offset}} \right) \times {BG}_{i}}}{\sum_{i = 1}^{n}{\alpha_{i} \times \beta_{i} \times \left( {{isig}_{i} + {offset}} \right)^{2}}}$

In addition, in a preferred embodiment, Alpha weights are fixed for eachBG entry in the calibration buffer such that the most recent BG entry(i.e., position 1) has a weight of 0.80, position 2 has a weight of0.13, position 3 has a weight of 0.05, and position 4 has a weight of0.02. In the preferred embodiment, Beta weights for each BG entry arecalculated using the equation as follows, with i indicating the positionin the calibration buffer:

beta(i)=2.655×(BG(i)−0.8041)−0.01812

The Cal Factor calculated is weighted with the expected_cf_value if thesystem is not in FDC mode and EIS has not detected a sensitivity change.The expected_cf_value carries a 20% weight and the calculated Cal Factorhas an 80% weight. The Expected Cal Factor is calculated as follows:

expected_cf_value=0.109*t+4.731

where t=days from sensor start. If the system is in the Isig DipCalibration mode, and the calculated Cal Factor is less than 75% of theCR, the Cal Factor is set to 75% of the CR. This ensures that the BG andSG values are reasonably close following a calibration during an IsigDip.

Individual WE SG Calculation

Sensor glucose values are calculated in accordance with the relation

SG=(fisig+offset)×calFactor+predictedSGchange

where The predictedSGchange value is a 5-minute predicted value that iscalculated based on the filtered Isig, and moderated based on signalnoise and glucose concentration. If the predictedSGchange is more than 6mg/dL or less than −6 mg/dL, it will be clipped at 6 mg/dL or −6 mg/dL,respectively. In addition, the calculated SG is rounded to two decimalplaces.

First Day Calibration Mode

As described previously, the First Day Calibration adjustment, referredto as FDC, addresses situations when the initial calibration factorindicates there is an abnormal calibration factor. While in FDC, thealgorithm will adjust the Cal Factor towards a target range. For entryinto FDC mode, if the first successful BG entry indicates thecalibration ratio is outside the normal range of 4.5 to 5.5 mg/dL/nA,but inside the calibration error thresholds, then the FDC mode for thatWE will be turned on. In this mode, the Cal Factor will be calculatedusing the most recent BG and fIsig, and then adjusted as set forthbelow.

When the First Day Calibration mode is active, the Cal Factor for thatWE will be adjusted on each 5 minute packet in accordance with:

cfAdjust=(p1×origCF+p2)×5/60

calFactor=calFactor+cfAdjust

where P1=−0.1721 hour−1, and p2=0.8432 mg/dL/nA/hour. First DayCalibration adjustment will not take place for the current packet ifeither: (1) cfAdjust is negative and the SG is already low (under 75mg/dL); or (2) the adjusted Cal Factor has reached target range (4.5 to5.5 mg/dL/nA).

FDC mode per WE will stop and no additional adjustment allowed for thesensor when 12 hours have passed since the start of the sensor, or a newcalibration entry has a CR within the stable range (4.5 to 5.5mg/dL/nA). While the system is in FDC mode, the calibration expirationtime is 6 hours. However, in connection with Smart Calibrations, if theinitial accepted calibration has a CR outside a wide range (under 4mg/dL/nA or above 7 mg/dL/nA) for both WEs, the first calibration willexpire in 3 hours.

Isig Dip Calibration Mode

Embodiments of the invention use Isig Dip Calibration logic in responseto certain calibrations which are suspected to occur on Isigs that arelow for the glucose concentration. The logic returns the Cal Factorcloser to the prior value. Isig Dip Calibration mode is turned on if theWE is not in the FDC mode and, at calibration, the calibration indicatesthat the Isig is low, and a prior calibration was successful. This isverified by comparing the following thresholds:

-   -   CR>1.4×previous calFactor (termed origCF)    -   Previous calFactor<6 mg/dL/nA    -   Average value of recent valid Isigs<20 nA        The fIsig value used to calculate the Cal Factor on the Isig Dip        is subsequently used in an adjustment logic as described below,        and will be termed triggerIsig. In addition, the previous Cal        Factor is used to determine if the Isig Dip Calibration mode        should exit. This previous Cal Factor is termed origCF.

If Isig Dip Calibration mode is on, Isig is monitored for recovery. Inan embodiment of the invention, recovery is detected when the currentfIsig value is more than 1.4×triggerIsig. Once a recovery is detected,the Cal Factor will be adjusted as long as the fIsig is abovetriggerIsig. The Cal Factor is adjusted at a rate which would return theCal Factor to the origCF value in 12 hours.

Isig Dip Exit

The algorithm will stop adjustment and exit the Isig Dip Calibrationmode if any of the following are true, where Cal Factor is the mostrecent (possibly adjusted) Cal Factor:

-   -   calFactor<origCF×1.2    -   calFactor<5.5

More than one day has passed since the detection of the Isig Dip.

A new BG at calibration time shows CR<1.25×origCF.

EIS Smart Calibrations

At every EIS measurement, a 5 point moving average filter is used tofilter the 1 kHz imaginary impedance. If it has been less than one hoursince the previous calibration, the expected 1 kHz imaginary impedancevalue of the previous calibration is set to the current filtered value,and the allowed range for the 1 kHz imaginary impedance value is setbased on recent EIS measurements. If it has been over one hour since theprevious calibration, and the current filtered impedance value isoutside the allowed range for both WEs, the calibration expiration timeis reduced to a maximum of six hours from the previous calibration. Ifcalibration is taking place when sensitivity change has been detected,then, if the CR is >15% different than the most recent CR in thecalibration buffer, only the new and previous BG are kept in thecalibration buffer, the expected_cf_value is not used to calculate theCF.

Working Electrode State

Each individual working electrode is assigned a state that determineshow information from that electrode is used for subsequent processing.The states are determined by various error checks, diagnostics, andcalibration statuses. The following table summarizes the states:

Description State Conditions Normal 0 Normal Intermediate 1 CalibrationRecommended Invalid 2 Discard; Invalid; Artifact Noise EIS Vcntr CalError Calibration Required

Noise

If two consecutive windows occur with high noise (per abovecalculation), the Isig data will be considered invalid (state=2) untilthe end of the two hour window (at which point the work electrode mayeither be terminated or this logic will no longer flag the data asinvalid). If three consecutive two hour windows occur with high noise(per above calculation), the work electrode state is set to 2irreversibly and is considered terminated.

EIS—Working Electrode Termination Based on 8 kHz Imaginary Impedance

At every EIS measurement, a 5 point moving average filter is used tofilter the 8 kHz imaginary impedance. The filtered value is monitoredfor 36 hours from sensor connection. After 36 hours, the minimum 8 kHzfiltered imaginary impedance value is set as the reference, excludingthe values taken during the warmup period. In a preferred embodiment ofthe invention, the latter reference value is clipped to the range:−1,000Ω to 800Ω. Once the reference is set, the absolute differencebetween the filtered 8 kHz imaginary impedance value and the referencevalue is calculated at every EIS measurement. The working electrodestate is set to 2 irreversibly and terminated if the difference islarger than 1,200Ω for two consecutive packets.

EIS—WE Termination and Error Based on 1 kHz Real Impedance

At every EIS measurement, a 5 point moving average filter is used tofilter the 1 kHz real impedance. The filtered real impedance value ismonitored until the filtered and unfiltered values are below 7,000Ω. Ifthe unfiltered 1 kHz real impedance value is above 10,000Ω, an error istriggered and the state is set to 2. If the condition persists for 3hours, the working electrode is terminated. If the filtered 1 kHz realimpedance is above 12,000Ω, the state is set to 2, and the workingelectrode is terminated.

Fusion

As described hereinabove in connection with FIG. 120, in a preferredembodiment of the inventions herein, the fusion algorithm proceeds asfollows: If both WE SGs are invalid or in state 2, then fusion SG is setas invalid. If only one WE SG is invalid or in state 2, then fusion SGis equal to the other valid WE SG. The fusion algorithm includes twomodes of weight calculation, and logic describing how to transitionbetween the two modes.

RMEM Fusion Mode

Rmem Fusion leverages the differences in Rmem on each working electrodeto determine fusion weighting. In general, the working electrode withthe lower Rmem will receive the greater fusion weight. In this regard,Rmem from each working electrode's EIS measurement is calculated priorto the latest successful calibration, and the values are stored.

Combined Cal Factor and Noise (CCFN) Fusion Mode

Combined Cal Factor and Noise Fusion mode use these two metrics todetermine fusion weight. Cal Factor Fusion leverages the Cal Factor oneach working electrode to determine fusion weighting. The Cal Factor oneach working electrode is transformed via a lookup table or functionwhereby CFs that are within a pre-defined range receive greater weight.Thus, to calculate the Cal Factor Weight (cfWeight1) metric, the CalFactor is transformed, as described hereinabove, such that extremevalues receive a weight of zero, optimal values receive a weight of one,and intermediate values receive weights between zero and one. Thetransform function is a normalized log-normal curve which is, as notedpreviously, defined by the parameters (Fusion) p, which describes theCal Factor transform log-normal curve peak, and (Fusion) a, whichdescribes the Cal Factor transform log-normal curve width. In preferredembodiments, p may have a value of 1.643, and a may have a value of0.13.

The output of the log-normal transform is saturated to [0.001,FUSION_CLIP], where the lower saturation limit is to prevent divide byzero errors downstream, and the upper saturation limit equalizes allscores above the parameter FUSION_CLIP. In a preferred embodiment,FUSION_CLIP may be set to 0.6. Finally, the transformed, saturated CalFactor for each working electrode is normalized by the sum across theworking electrodes, and the ratio is passed through the ratioGainfunction.

Noise-Based Fusion

Noise Fusion leverages the differences in noise on each workingelectrode to determine fusion weighting. In general, the workingelectrode with the lesser noise will receive the greater weight. Thefiltered noise from each working electrode is calculated via a movingaverage filter of length FUSION_NOISEWINDOW on the absolute value of thevariable containing the second derivative of the raw Isig (acc_rawisig)from each working electrode. In a preferred embodiment,FUSION_NOISEWINDOW is set to 36 hours. It is noted that, prior to theavailability of FUSION_NOISEWINDOW number of packets (e.g., duringwarmup), the moving average filter length is equal to the number ofavailable packets.

Next, in order to avoid dividing by zero, each WE's filtered noise valueis saturated such that if filteredNoise<0.001, then filteredNoise=0.001.Then, a Noise Weight Metric is assigned to each WE by using the otherWE's saturated filteredNoise value, normalized by total noise. Asdescribed in detail hereinabove, in this way, the WE with the lowernoise receives a greater weight. Finally, the Cal Factor and Noisemetrics are combined as set forth above in connection with FIG. 119.

Fusion Mode Transition

Different modes of Fusion may be appropriate for the sensor depending onthe sensor's status. The Rmem fusion mode is generally most appropriateearlier in the sensor wear. The Cal Factor and Noise fusion is mostappropriate later in wear. In order to transition between these modes offusion, in a preferred embodiment of the invention, afterFUSION_START_TIME_SWITCH, fusion weighting is completely determined byCCFN. This Time Scheduled Switching logic supersedes Rmem SimilarityTransitioning.

Rmem Similarity Transitioning

The logic for transitioning fusion mode depends on the similaritybetween the WE Rmem values. A large difference in Rmem means the finalfusion value is to be dominated by Rmem based fusion. As the differencein Rmem values approaches zero, Rmem fusion weights approach 0.5. Atthis point, it is appropriate for Combined Cal Factor and Noise Fusion(CCFN) to have a greater influence on final fusion weights. Fusionweight values are calculated as shown, e.g., in FIG. 119.

Fusion Weight Smoothing

A symmetric weighted moving average is applied to the fusion weightvalues after being computed. This avoids sharp transitions in caseswhere sharp transitions occur due to one of the working electrodesbecoming unreliable. Sharp transitions are allowed at calibration. Forthis purpose, the coefficients of the filter are: [1 2 3 4 4 3 2 1]/20.

Fusion SG Calculation and Display

When fusion is enabled, the fused SG value is the final weighted sum ofthe plurality of working electrode SGs. Thus, for a system with 2working electrodes:

filteredRi_2(t)=1−filteredRi_1(t)

fused_sg(t)=(filteredRi_1(t)×cur_sg(1)+filteredRi_2(t)×cur_sg(2))

where filteredRi_1(t) is the filtered fusion weight for WE1, and thefused SG value is rounded to 0 decimal places. It is noted that, in apreferred embodiment, the displayed fusion SG must be within the range[40, 400]. If the calculated fusion SG is below 40 mg/dl, the displaywill show “<40 mg/dl”, and if the calculated fusion SG is above 400mg/dl, the display will show “>400 mg/dl”.

Fusion Rate of Change (ROC) Calculation

The SG rate of change may be calculated on every 5 minute packet. Here,roc1 and roc2 are first calculated as follows, using the three mostrecent fusion SG values, where fused_sg(1) is the most recent fusion SGvalue:

roc1=(fused_sg(1)−fused_sg(2))/5

roc2=(fused_sg(2)−fused_sg(3))/5

If the direction (sign) of roc1 is different from roc2, or any of themost 3 recent SGs is blanked for SG display, the SG rate of change isset to zero mg/dL/min. Otherwise, the fused_sg rate of change is thevalue of roc1 or roc2 that is closer to zero.

Calibration BG Request and Coordination

Individual WEs can trigger calibration BG requests. However, inembodiments of the inventions herein, the user will be prompted forcalibration BG requests only when all functioning WEs have calibrationrequests outstanding. An exception to the foregoing is the firstcalibration request, which is to occur at or after SENSOR_WARMUP_TIME,as discussed previously. Here, the user will be prompted for the firstcalibration BG request when any functioning WE has calibration requestsoutstanding.

Calibration may be displayed to the user as either “recommended”, or“mandatory”. “Calibration recommend” logic is triggered according to thecalibration schedule (i.e., 2 calibrations per day plus smart cals, in apreferred embodiment). As noted, EXTRA_TIME is allowed to lapse beforecalibration becomes mandatory and SG computation stops. This time is setto EXTRA_TIME_SMART when a calibration is caused by a smart cal. Basedon when a smart cal is triggered relative to the last successfulcalibration, data may continue to be displayed for 6-12 hours. The stateof the SG is recorded so that the display device may determine if or howto display the SG during “calibration recommended” states. The tablebelow is a graphical representation of the logic:

WE1 WE2 Fusion Calibration State Calibration State Calibration StateNone None None None Recommended None None Mandatory None Recommended*Recommended* Recommended* Recommended* Mandatory Recommended* MandatoryMandatory MandatoryIt is noted that the states in the table above are summarized forbrevity. Thus, the complete logic table can be generated by switchingWE1 and WE2. In addition, the user is exposed only to the “fusioncalibration” state.

As has been discussed in detail herein, most continuous glucose sensormonitoring (CGM) systems require finger-stick blood glucose measurementsfor calibration. For real-time systems, it can be difficult to determinechanges in sensor behaviors, such as sensitivity or sensor anomaly, atthe time of the data output. Therefore, calibration using a finger-stickmeasurement is needed to assure sensor accuracy. Calibration usingfingersticks, however, is not only painful, but also cumbersome for theuser. Embodiments of the inventions herein, therefore, may employretrospective calibration-free algorithms for continuous sensorrecorders, including use of the ASIC previously described in detailherein. In this regard, as was noted previously in connection withEIS-related algorithms and calibration, within the context of theinventions herein, the term “calibration-free” does not mean that aparticular sensor needs no calibration at all. Rather, it means that thesensor can self-calibrate based on the data that is stored in the sensorrecorders, without the need for additional finger-stick or meter data.Thus, the need for finger-stick measurements to provide a reference canbe eliminated for retrospective systems.

Retrospective sensor systems have the ability to have the entire tracesof raw signals available for use by an algorithm before processing andconverting to glucose values. Specifically, sensor recorders may recordthe raw signals, such as, e.g., Isig and Vcntr, as well as EIS data fordiagnostics. As shown in FIG. 121, the retrospective algorithm maycomprise several processing components, including: (1) raw Isig signalprocessing (9405, 9410); (2) discrete wavelet decomposition of the rawIsig signal (9415); (3) raw EIS signal processing (9430, 9435); (4)generating sensor glucose (SG) based on different models from machinelearning methods (9440, 9445); (5) fusion of the SG values fromdifferent models (9450); (6) selective filtering (9463); and (7)blanking of SG (9455, 9460).

The processing of the raw Isig signal may use a unified and simplifiedfunction to handle several anomalies such as artifacts and noisysignals. In addition, signal smoothing (9420) may be accomplished byusing a polynomial model for local regression with weighted linear leastsquares. Effects of outliers are reduced by assigning less weight.Retrospective processing allows local regression to be done with forwardand backward data, with the smoothing having no phase delay as seen inmost real-time filtering. Following the smoothing, noise calculation isperformed. Noise calculation (9425) is based on evaluating thedifference between the raw and smoothed signal, and calculating thepercentage of data within a defined window that has high noise-to-signalratio. EIS data may also be smoothed using a similar retrospectivesmoothing function (9435). After smoothing of the EIS data, the EIS datamay then be interpolated to generate EIS data that match the timestampsof the Isig data.

In a preferred embodiment, discrete wavelet transform is applied on theraw Isig signals (9415). The transform operation decomposes the Isigsignal into several predefined levels. At each level, the algorithmgenerates the coefficients for approximation and detail signals, wherethe approximations are the high-scale, low-frequency components of thesignal, and the details are the low-scale, high-frequency components ofthe signal. For the approximation signals, the lower level approximationcaptures the short term variations and the higher level approximationcaptures the long term trend. Discrete wavelet transform may also beused as a valuable tool in identifying regions with sensitivity loss inthe signal.

Machine learning techniques, e.g., can be used to generate the modelsfor converting signals into SG values (9440) as a function of measuredsignals (e.g., Isig, Vcntr, EIS, etc.). In preferred embodiments, threespecific techniques may be used, including genetic programming (GP),artificial neural network (NN), and regression decision tree (DT). Togenerate the training data set, blood glucose (BG) measurement valuesand the associated Isig, Vcntr, wavelet and EIS data points areextracted. Preprocessing of the data can also be done to improve themodel being generated. Preprocessing steps include reducing the numberof data points that are close in time, adjusting the distribution ofpoints within a certain glycemic range to reduce overemphasis at that(BG) range, and removing outliers to reduce/eliminate BG points withhigh variations.

Genetic programming (GP) is based on rules that imitate biologicalevolution. Combining basis functions, inputs, and constants creates aninitial model population. The models are structured in a tree-likefashion, with basis functions linking nodes of inputs. In eachgeneration (iteration) of the algorithm, relatively successfulindividuals are selected as “parents” for the next generation and form areproduction pool. New generations of solutions evolve, using one ofthree possible operators: crossover, mutation, and permutation. Theprocedure is repeated until a stopping criterion is attained. In anembodiment of the invention, examples of training results may include:

GP1:

sg=(u2*A ₁*((u1+A ₂ *u6)*u33))−A ₃

GP2:

sg=(u4̂2−A ₄ *u ₄ −A ₅ *u45−A ₆ *u2)*A ₇ +A ₈ *u1−A ₉

GP3:

sg=((u4̂2)̂2−A ₁₀*(u2+A ₁₁ *u43))*A ₁₂ +A ₁₃ *u1−A ₁₄

where A₁-A₁₄ are constants that are learnt by the modeling (e.g.,machine learning), and where u1, u2, u4, u6, u9, u33, u43, and u45 maybe values of Isig, Vcntr, time since connection, and/or EIS features(e.g., real and/or imaginary impedance) measured at frequencies between0.105 Hz and 8 kHz.

Neural networks are composed of simple elements operating in parallel.These elements are inspired by biological nervous systems. As in nature,the connections between elements largely determine the network function.A neural network model is trained to perform a particular function byadjusting the values of the connections (weights) between elements. Theback propagation (BP) neural network algorithm, a multi-layerfeedforward network trained according to error back propagationalgorithm, may be used, with inputs including, e.g., Isig, Vcntr, EIS,wavelets, duration (i.e., time since sensor insertion), etc., to producea BG output.

In a decision tree, the model is comprised of several nodes in whichsplitting of the population occurs and the output is comprised ofseveral regression models. For a numeric prediction, a regression treemay be used which, in turn, uses measured inputs (including, e.g., Isig,Vcntr, EIS, wavelets, etc.), to produce a BG as output in the training.Initially, a starting tree is built from top down. At each node, adecision is made on a variable and split into subsets. Splitting isbased on maximizing the purity of each node. The results at the bottomare the leaves, wherein each leaf is a linear model relating the SG withthe input variables. Pruning can be done to reduce the number of splits.

FIG. 122 shows an example of a decision tree in accordance with anembodiment of the inventions herein. Starting with measured Isig inblock 9502, a determination (i.e., decision) is made as to whether themeasured Isig value is ≤34.58 nA (9504), or >34.58 nA (9506). If thelatter is true, then a further decision is made as to whether the Isigvalue is ≤48.82 nA (9504), or >48.82 nA. If the former is true, then theSG may be calculated according to a Linear Model (LM5), as shown inblock 9520. If, on the other hand, Isig is >48.82 nA, then SG may becalculated according to a different Linear Model (LM6), as shown inblock 9522.

Returning to block 9504, when Isig is ≤34.58 nA, a further decision ismade as to whether Isig is ≤19.975 nA (9508). If it is, then, ifVcntr≤−0.815V, then a first Linear Model (LM1) is employed (9512).Otherwise (i.e., if Vcntr>−0.815V), then a second Linear Model (LM2) isused (9514). If, on the other hand, Isig>19.975 nA, then a furtherdecision is made at block 9510. Here, if wavelet10 (w10)≤27.116, then athird Linear Model (LM3) is used (9516). However, if wavelet10>27.116,then a fourth Linear Model (LM4) is used to calculate SG (9518).

Fusion of the SGs may be performed to generate a single output SG. Ashas been discussed hereinabove, fusion may be done by assigning weightsto each of the SGs based on various inputs, and then combining theoutputs. In preferred embodiments of the invention, such inputs mayinclude EIS, Isig, duration, and wavelets. Other methods for signalfusion may also be utilized.

In one preferred embodiment, blanking of the data may be performed onthe final SG to prevent displaying of unreliable signals. Blanking basedon noise is done by setting thresholds on the noise level and blankingthe data above the threshold. Blanking based on EIS, Isig, Vcntr, andwavelets may also be performed. A decision tree may also be used togenerate blanking models that combine the various inputs. For example, adecision tree may be used to identify “good” or “bad” points in atraining set. In an embodiment of the invention, a threshold may be seton Cal Ratio (as a good indicator of sensitivity loss), with pointshaving a Cal Ratio above the threshold identified as “bad” points.

FIG. 123 shows an example of training results with Isig, Vcntr, and twowavelets (w7 and w10) as inputs, in accordance with embodiments of theinventions herein. If w7 is less than or equal to a first threshold, andVcntr is greater than a second threshold, then the signal may be shown(9550, 9552, 9556). However, if Vcntr is less than or equal to thesecond threshold, then the signal will be blanked (9554). As shown onthe right-hand side of the decision tree, if w7 is greater than thefirst threshold, and w10 is greater than a third threshold, then thesignal may be shown (9558, 9562). Similarly, if w10 is not greater thanthe third threshold, but the Isig is greater than a fourth threshold,then the signal may still be shown (9560, 9566). Moreover, if w10 is notgreater than the third threshold, and Isig is not greater than thefourth threshold, but Vcntr is greater than a fifth threshold, then thesignal may still be shown (9560, 9564, 9570). However, if Vcntr is lessthan or equal to the fifth threshold, then the signal will be blanked(9568).

In embodiments of the invention, an outlier detection algorithm may beused as a diagnostic tool, including fusion, selective filtering, andblanking of data. Specifically, the fusion algorithm may fuse sensorglucose values from, e.g., a decision tree (DT) algorithm and geneticprogramming (GP), based on approximated error difference. Selectivefiltering entails filtering of the fused SG values and spike removal. Ablanking algorithm may be based on approximated error prediction.

More particularly, the above-mentioned fusion algorithm includesexamining the difference between decision tree Absolute RelativeDifference (ARD) and genetic programming ARD at each BG point, as eachof DT and GP has respective areas with better performance. Thedifference is then fit by a linear regression combination of parameters,inputs, and functions of parameters, including, e.g., SG, CR, imaginaryimpedance, real impedance, noise, rate of change, sensor gain,cumulative Vcntr rail time, etc. Thus, e.g.:

ARD _(DT) −ARD _(GP)=Σweight_(n)×param_(n)

where the parameter list and weights are updated with every iteration ofDT and GP. The parameters are automatically pruned one by one based onremoving the lowest sensitivity, until a final set of parameters andcoefficients is obtained. The expected difference is then transformedinto a weight ([0,1]) for DT and GP for generating a weighted average ofSG values:

${w\left( {ARD}_{diff} \right)} = \frac{1}{1 + e^{{kARD}_{diff}}}$

Selective sensor glucose (SG) filtering allows noisy segments of SG tobe smoothed, rather than blanked, so that SG display may continuewithout disruption. Thus, selected sections may be smoothed using afilter that turns on at high noise. In this regard, in embodiments ofthe inventions herein, spikes in SG may be detected by the secondderivative and removed, with SG selectively smoothed by, e.g., a12-point, low-pass infinite impulse response (IIR) filter on lowsignal-to-noise ratio (SNR) points.

As noted, a blanking algorithm may be based on approximated errorprediction, i.e., model prediction of error at each point. In thisregard, coefficient weights may be generated by fitting the model to ARDat each BG point in training data. Thus:

${ARD}_{expected} = {C_{0} + {\sum\limits_{n = 1}^{n}{{C(n)}{{param}(n)}}} + {{abs}\left( {\sum\limits_{m = 1}^{M}{{C(m)}{{Param}(m)}}} \right)}}$

where SG is blanked when expected ARD is above a threshold. FIG. 124shows examples of parameters that may be used in a blanking algorithmbased on approximated error prediction. As shown in FIG. 125, diagnosticsteps progressively decrease MARD and increase consensus while, at thesame time, ensuring that sensor display times remain high at about 98%after blanking.

In embodiments of the inventions herein, the foregoing algorithms mayalso be applied to real-time systems, where real-time information (e.g.,Isig, Vcntr, real-time EIS with zeroth-order hold, etc.) may be used asinputs. In contrast to the retrospective algorithms, real-timealgorithms may be generated that do not use interpolated EIS orwavelets.

In one embodiment, the present inventions are directed to systems andalgorithms for augmenting a calibration-free sensor glucose (SG) readingwith an optional calibration using blood glucose (BG) value(s).Specifically, the logic of such an algorithm includes methods forproviding such augmentation via asynchronous blood glucose (BG)calibrations at, e.g., 5 minute intervals. The logic is designed suchthat SG readings will continue to occur when no BGs are available—asdescribed hereinabove, e.g., in connection with retrospectivecalibration methodologies, and/or implementation of such methodologiesin real-time systems. However, when BG values are available, they may beentered, and the logic integrates the information from the BGcalibration to modulate current and future SG readings.

As was noted previously, the current state of continuous glucosemeasurement (CGM) requires that a patient measure his/her blood glucose(BG) using a test strip meter to calibrate the CGM system. Such externalcalibrations, however, are disadvantageous for various reasons. First,test strips are an extra expense for users to manage their diabetes.Second, finger sticks cause pain and discomfort to the user. Third,calibrations via BG meters are also prone to user error, whether sucherrors are unintentional, such as taking a measurement after handling asugary substance, or intentional, such as inputting a false calibrationin the CGM system to avoid taking a finger stick. Fourth, BG meters arenot perfectly accurate and include inherent error even with perfect use.Finally, existing calibrated CGMs require a strict calibration regimento keep the sensor accurate. As has been detailed herein, variousmethodologies have been introduced to minimize or eliminate the numberof finger sticks necessary for calibrations.

In one such methodology, calibrations are eliminated by using EIS inaddition to sensor models generated by machine learning algorithms.However, there are various limitations that make calibrations by a BGmeter still useful. For example, variability in sensors manufactured cancause unexpected shifts in sensor sensitivity which may not be accountedfor by sensor models. Sensitivity loss over time, while accounted for insensor models, is subject to patient physiology and other unknownfactors that cannot be perfectly modeled. The sensor models generatedmay also be limited to the patient and sensor data available during thetime of algorithm development, and thus have difficulty extrapolating topatients with vastly different sensitivity.

To address the foregoing, embodiments of the invention areadvantageously directed to a hybrid approach, whereby (external, BG−)calibrated and calibration-free sensor glucose algorithms may becombined to provide an optional calibration system and methodology.Here, the CGM system is configured to show a SG reading regardless ofinput calibrations. However, unlike existing calibration-free systems,users are able to calibrate their sensor if they notice that theirreadings are not accurate. Compared to (externally) calibratedalgorithms, advantages of an optional calibration system includeflexibility for users to calibrate their system when they choose to doso, reduction in required calibrations, and accessibility fornon-insulin requiring diabetics who do not need a blood glucose meter.Compared to calibration-free algorithms, advantages include higheraccuracy with minimal calibrations and robustness to patient and sensorvariability.

FIG. 126 shows a diagram of an optional calibration logic within acalibration-free algorithm in accordance with a preferred embodiment ofthe invention. The physical system required for the CGM system withoptional calibration logic includes the physical sensor electronics, amicrocontroller, a transmitter, and at least one working electrode. Asshown in FIG. 126, the sensor records the working electrode current(Isig) and voltage of the counter electrode (Vcntr), 9610, as well asEIS signals 9612, at regular intervals. After optionally preprocessingthe (raw) Isig and Vcntr values (9614), a SG reading is generated foreach Isig value in real-time (9620). In order to track sensitivity loss,moving averages and low-pass (e.g., Butterworth) filters are applied tothe Isig signal (9616) to track long-term trends in sensor sensitivity.This approximates wavelet decomposition used for tracking sensitivityloss in retrospective systems, although the real-time filters containsignificant phase-lag.

Optional calibration logic takes the SG approximation from one or morecalibration-free models at a regular interval (e.g., every 5 minutes)and BG calibrations whenever available. Each calibration-free model maybe a machine learning or analytical model that can generate a SG readingfor each Isig reading (9620). SG models may take the form of analyticalmodels derived from theoretical sensor dynamics or by machine learningmodels generated empirically from existing sensor data. In preferredembodiments, the machine learning models used include geneticprogramming, regression decision trees, and bagged decision trees. Togenerate the training data set for training the SG models, BGmeasurement values (9630) and the associated Isig, Vcntr, EIS data,low-passed Isig filtering, and time from sensor connection areextracted. Preprocessing may be done to improve the models beinggenerated. Preprocessing steps may include down-sampling data that isclose together in time, adjusting the distribution of points withinoversampled glycemic ranges, and removing outliers for BG and inputfeatures. If a model cannot accurately predict a SG value for an Isigreading, the model may output a placeholder value and flag the data asinvalid.

Each SG reading from each model is accompanied by a variance estimate ofthe SG reading (9642). Variance estimates may be obtained empiricallyfrom training data and applied to the model SG values through a look-uptable or fitted analytical function. SG readings from each model arethen fused using Gaussian univariate fusion to obtain the fused SGreading (9646). When a BG is available, the information of the BG may beincorporated in two ways: adjusting the SG of each model prior tofusion, and adjusting the fused SG post-fusion.

Specifically, the SG from each model is compared to the BG. SG modelsthat deviate from the BG have their output SG value and expectedvariance modulated for a period of time after calibration (9644). OutputSG values are scaled or offset to bring the values closer to thecalibration BG, and expected variance is increased for larger deviancesbetween model SG values and calibration BG values. In a preferredembodiment of the invention, an example of this modulation can beexpressed via the following equations:

$\frac{{BG} - {SG}_{model}}{Isig} = M$SG_(Adjusted) = (M)(Isig)(e^(−C₁t)) + SG_(Model)$\sigma_{Adjusted}^{2} = \frac{{A\left( {{BG} - {SG}_{Model}} \right)}^{2} + \sigma_{SG}^{2}}{A + 1}$

Where SG_(Model) is the output of one of the SG models, BG is the inputBG value, M is a modulation factor set during calibration. For timeafter calibration, t, SG_(Adjusted) is the SG adjusted after calibrationwith decaying weight based on time constant, C₁. As shown in the thirdequation above, adjusted variance, σ² _(Adjusted), is calculated by aweighted average of the squared error between BG and SG_(Model) and theexpected variance of the model SG, σ² _(SG). In this equation, “A”represents the weighting constant for the squared error of BG, and canbe any positive value (e.g., 2). In another embodiment of the invention,an alternative example of the above-described modulation may beexpressed via the following equations for use in optional calibrations:

$\frac{BG}{{SG}_{Model}} = M$ SG_(Adjusted) = M e^(−C₁t) * SG_(Model)$\sigma_{Adjusted}^{2} = \frac{{A\left( {{BG} - {SG}_{Model}} \right)}^{2} + \sigma_{SG}^{2}}{A + 1}$

where components of these equations are defined in the same manner asthose that are described immediately above.

A Kalman filter 9648 can then be applied to merge the SG post-fusionwith the BG values. The Kalman filter contains two sets of measurementfunctions for when a calibration is available and when a calibration isunavailable. The Kalman filter states contain at least two states forthe estimated SG and a modulation factor that takes the form of a gainor offset. When no calibration is available, the measurement functionsuse the fused SG to adjust the estimated SG state. When a calibration isavailable, the measurement functions use the fused SG and thecalibration BG to adjust both the estimated SG state and the modulationfactor. An unscented Kalman filter is used for non-linear process andmeasurement functions. An additional benefit to using the Kalman filterat this stage is that the signal is smoothed, which may be necessary iffusion causes sudden jumps between models. In embodiments of theinvention, an example of the Kalman filter implementation may beexpressed by the following functions:

States:

$X = \begin{bmatrix}{SG} \\{dSG} \\G \\{IG}\end{bmatrix}$

Process Model Functions:

$F = \begin{bmatrix}{{SG} + {dSG}} \\{dSG} \\G \\{{IG} + {C_{1}\left( {{SG} - {IG}} \right)}}\end{bmatrix}$

Measurement Functions:

H _(Isig)=[IG]

H _(BG)=[SG,dSG,G,IG]

Measurement Inputs:

  Z_(Isig, n) = [SG_(fused)(ISIG_(n)) + G * ISIG_(n)]$\mspace{20mu} {{newG} = \frac{{BG} - \left( {{{DT}_{SG}({ISIG})} + {C_{2}{dSG}}} \right)}{ISIG}}$$Z_{{BG},n} = \begin{bmatrix}{BG} \\{{{DT}_{SG}\left( {ISIG}_{n} \right)} - {{DT}_{SG}\left( {ISIG}_{n - 1} \right)} + {{newG}\left( {{ISIG}_{n} - {ISIG}_{n - 1}} \right)}} \\{newG} \\{{{DT}_{SG}\left( {ISIG}_{n} \right)} + {{newG}*{ISIG}_{n}}}\end{bmatrix}$

Initialized States and covariance

${X(0)} = \begin{bmatrix}{{SG}(1)} \\0 \\0 \\{{SG}(1)}\end{bmatrix}$ ${P(0)} = \begin{bmatrix}30 & 0 & 0 & 0 \\0 & 30 & 0 & 0 \\0 & 0 & 10 & 0 \\0 & 0 & 0 & 90\end{bmatrix}$

Process Noise Covariance Matrix:

$Q = \begin{bmatrix}0.25 & 0.5 & 0 & 0 \\0.5 & 1 & 0 & 0 \\0 & 0 & 0.003 & 0 \\0 & 0 & 0 & 30\end{bmatrix}$

Measurement Covariance Matrix

R_(Isig) = 500 $R_{BG} = \begin{bmatrix}50 & 0 & 0 & 0 \\0 & 30 & 0 & 0 \\0 & 0 & 7 & 0 \\0 & 0 & 0 & 37\end{bmatrix}$

In connection with the above, the states are defined as follows: SGrepresents the sensor glucose output; DT_(SC) represents the SG of adecision tree output (see, e.g., FIG. 122); dSG represents the rate ofchange of sensor glucose; G represents the gain function for modulationof sensor glucose; and IG represents interstitial glucose. H_(Isig),Z_(Isig), and R_(Isig) are the measurement functions and covarianceswith no calibration and only directly adjust the IG state. H_(BG),Z_(BG), and R_(BG) are the measurement functions and covariances when aBG calibration is available and adjust all states to shift thesensitivity of the sensor. C1 and C2 are constants, wherein C1 is theexchange rate of glucose from blood to interstitial glucose for atwo-compartment model, C2 is a decay constant for the state G, and bothC1 and C2 are constrained to values [0,1].

A different set of process functions may be used in the first day ofwear, where sensor instability is expected. The gain calculated fromcalibrations on the first day may not be appropriate. The processfunction for the state G is replaced with G-C₂G which steadily decreasesthe influence of first day calibrations. The process function for day 1may then be described as follows:

$F_{{day}\; 1} = \begin{bmatrix}{{SG} + {dSG}} \\{dSG} \\{G - {C_{2}G}} \\{{IG} + {C_{1}\left( {{SG} - {IG}} \right)}}\end{bmatrix}$

As shown in FIG. 126, the output from the Kalman filter may then beprocessed through an error detection logic 9652, and a final SG value9662 calculated.

As noted previously, embodiments of the present invention are alsodirected to complex redundancy in glucose sensors, systems, andassociated methods, including implementation of such redundant sensorsand/or systems within the context of the methodologies and algorithms(e.g., EIS, calibration, fusion, diagnostic, etc.) that have beendiscussed in the instant specification and associated diagrams. Morespecifically, and in view of the ASIC design, as well as the EIS andfusion methodologies that were detailed hereinabove, embodiments of theinventions herein are directed to sensor system configurations andalgorithms that seek to achieve stable, longer-wear glucose sensors thatalso provide fast run-in (i.e., fast startup, or stabilization) and canbe calibration-free.

In this regard, it is known that, in current sensor technology, thereexists a trade-off between fast startup, sensor longevity, and theaccuracy of a calibration-free algorithm. By way of illustration, FIG.127 shows a table of comparison between two different glucose sensordesigns (configurations), the “E3” and the “H1”, by Medtronic Minimed.As shown in FIG. 127, the E3 sensor provides for fast run-in (i.e.,time-to-stability) and is amenable for use with a calibration-freealgorithm. Its serviceable life, however, may be limited to about 7days. The H1 sensor, on the other hand, has a thicker GLM than that ofthe E3 sensor's which, in turn, allows for longer wear (sensorlongevity) of up to about 10 days. However, the thicker GLM alsonecessitates a longer startup timeframe (i.e., slower run-in), andreduces the diagnostic ability of an EIS algorithm for calibration-freeoperation.

To address the aforementioned tradeoffs, embodiments of the presentinventions are directed to glucose sensor systems that employ complexredundancy in such a way as to take advantage of the beneficialcharacteristics of non-identical, or dissimilar, sensor designs in acomplementary fashion. As was discussed previously, a sensor systememploying complex redundancy includes two (or more) sensors, of which(at least) two of the sensors are dissimilar to one another in design(and may also employ different chemistry and/or size). With reference tothe illustrative example of FIG. 127, one (or more) of the sensors maybe designed to have, e.g., considerably better hydration and/orstabilization characteristics, but a shorter lifetime, whereas the othersensor(s) may have long-lasting durability, but slow initial hydrationand/or stabilization. In such a case, in accordance with embodiments ofthe present inventions, a glucose sensor system and an algorithm may bedesigned whereby the first sensor(s) is used to generate glucose dataduring early wear, after which the first sensor(s) may be used tocalibrate the second sensor(s), and then a switch-over may be made(e.g., via the ASIC) to the second sensor(s) for generating glucose dataduring the remainder of the life of the glucose sensor system.

FIG. 128 shows an illustrative example, wherein a first sensor (E3) maybe used during early wear to generate sensor glucose (SG) values using acalibration-free algorithm, after which the first sensor may be used tocalibrate the second sensor (H1) once the latter has stabilized. Duringthis (mid-wear) period of time, sensor diagnostics, such as, e.g., EISdata, may then be used to determine the best way to fuse the respectiveoutputs of the first and second sensors. Finally, during the latter partof sensor wear, a determination may be made as to when the first sensoris no longer reliable, at which point a switch-over may be made to thesecond sensor for generating glucose data during the remainder of thelife of the glucose sensor system. Thus, in such a system, a fusionalgorithm, such as, e.g., those that were described previously indetail, may be used—in conjunction with the ASIC, which was alsopreviously described in detail—to provide for fusion of data from all ofthe working electrodes that are employed in the two (or more) sensors,as well as the switchover from the first sensor to the second sensor.

In the above example, the basic assumption is that one sensor may betailored to allow calibration free sensing (e.g., by having betterdiagnostics, more predictable behavior, and/or better manufacturingcontrol), while the other sensor may have different properties (e.g.,greater effective sensor lifetime), even though it may not suitable forcalibration free sensing. Advantageously, the foregoing allows for afast-startup, long-wear, calibration-free sensor system, wherein theuser/patient remains unaware that data was fused, or that aswitched-over was implemented between individual sensors duringmid-wear. Thus, in embodiments of the inventions herein, complexredundancy may be leveraged to achieve a calibration-free system thatstarts fast, lasts long, and, therefore, significantly reduces userburden by greatly reducing the need for reference blood glucose (BG)measurements.

In the ensuing discussion, reference is made to several diagrams indescribing the various features of the inventions herein. In thisregard, it is noted that, while the examples shown in the diagrams mayutilize two sensors, this is by way of illustration, and not limitation.Thus, the examples, devices, systems, and algorithms that are discussedhereinbelow may be extended to employ any number of sensors, as well allcombinations of calibrated/non-calibrated sensing amongst the totalnumber of sensors.

A basic block diagram is shown in FIG. 129, including a calibrated model9710, and a non-calibrated model 9720. As shown in FIG. 129, thedifference between the calibrated and non-calibrated models is thereference glucose value 9712 that may be used to calibrate the system.In the non-calibrated model 9720, the sensor glucose is estimatedwithout this reference value.

As has been described in detail hereinabove, traditionally, thereference glucose value 9712 is obtained from an external blood glucose(BG)—i.e., fingerstick—measurement. In the instant invention, however,where one goal is to reduce the number of fingersticks that patients areasked to take throughout sensor wear, the reference glucose value 9712is the output from a sensor also. Nevertheless, either or both of thecalibrated and non-calibrated models may also make use ofadditional/optional reference glucose values 9714, 9724, which may beobtained via a fingerstick, and which may be identical, or different foreach of the calibrated and non-calibrated models.

Inputs 9716, 9726 can be all signals that are used in either thecalibrated and non-calibrated models. Thus, this may include, e.g., thesensor current (Isig), one or more EIS signals, timestamps, Vcntr, othermeasured diagnostics, biometrics, etc. In the inventions herein, theinputs will relate to any combination of all possible inputs; that is, asubset may be abstracted and utilized from all of the actual inputs, inorder to calculate sensor glucose (SG) values 9718, 9728.

It is important to note that, within the context of the instantinvention, the actual calibration and calibration-free models may betreated as “black boxes”, as embodiments of the invention are directedto the manner in which such systems/models are combined to produce SGvalues, and not necessarily to the details of the models themselves.Thus, for purposes of the instant inventions, embodiments thereof mayemploy calibrated models which employ, for example, a linearrelationship between reference BG and sensor current, and/ornon-calibrated models which, for example, may be derived using machinelearning relating all inputs to the sensor glucose, examples of whichwere discussed previously in detail. Other models, as also discussedhereinabove, may also be employed.

Similarly, embodiments of the invention may employ one or more of thefusion algorithms which have been described hereinabove to generate afused sensor glucose value. In other words, in embodiments of theinvention, “fusion” may be defined generically, as a specific fusionlogic need not be referenced. What is significant, however, is thefunction of the fusion algorithm in embodiments of the invention, i.e.,to make a determination as to how best to combine the sensor glucoseoutputs from multiple sensors into a single (fused) system sensorglucose value for display to the user/patient. As noted previously, suchdetermination, in turn, will depend on the properties of each of thesensors. For example, if a first sensor is designed to perform betterearly in sensor wear, and a second sensor is designed to work betterlater in wear, then the role of fusion is to decide when to switch overfrom the first sensor to the second sensor, or how to ensure asharp/smooth transition between the respective SG outputs of the firstand second sensors. Thus, as shown, e.g., in FIG. 130, the fusion logic9730 uses respective inputs and SG values from each of the first andsecond sensors to generate a single, fused system glucose value 9735.Here, it is noted that all inputs available to the calibrationmodels—e.g., inputs 9716, 9726—are also available to the fusionlogic/algorithm 9730, where the inputs can be used as diagnostics tocompute the optimal combination of SG values from the multiple sensors.

With the above in mind, several illustrative embodiments of theinventions herein will now be described with reference to FIGS. 131-134.FIG. 131 shows a system in which a first sensor 9740 is non-calibrated,and a second sensor 9750 is calibrated. In this embodiment, no referenceblood glucose (i.e., external BG) is required. Specifically, in thisembodiment, the first sensor 9740 is designed in a way in whichcalibration-free operation is robust, whereas the second sensor 9750still needs a reference glucose value to compute SG. The output of firstsensor, therefore, can be used as a reference glucose value 9745 tocalibrate the second sensor 9750. The fusion algorithm 9730 then decideshow to optimally combine the respective SG outputs 9742, 9752 of thefirst and second sensors to generate a single, fused sensor glucosevalue 9735.

To summarize, in the embodiment shown in FIG. 131, the first sensor 9740has properties that allow the sensor to start up quickly afterconnection and, as such, has a suitable design for a calibration-freemodel. The first sensor 9740 can therefore be used to start SG displayto the user/patient at the beginning of sensor life. However, theproperties that allow the first sensor to be calibration-free alsoresult in a shorter effective lifetime than that of the second sensor9750. Therefore, the first sensor could be used to start the sensordisplay, and when the second sensor is ready, the output 9745 of thefirst sensor 9740 is used to calibrate the second sensor 9750. Thefusion logic 9730 decides on the transition time, which can be timebased, can be a smooth transition, or can use inputs/diagnostics 9744,9754 from the first and second sensors to estimate the optimal time andmethod of transitioning between the two sensors.

In another embodiment, shown illustratively in FIG. 132, both the firstsensor 9760 and the second sensor 9770 are non-calibrated (i.e.,calibration-free), and no reference blood glucose (i.e., external BGreference value) is required. However, the two sensors complement eachother. More specifically, in this embodiment, although both sensors arecalibration-free, the output of each calibration-free model may be usedto complement the other sensor's model. Thus, the output 9765 of thefirst sensor 9760 may be used as an optional reference glucose value forthe second sensor 9770, and/or the output 9775 of the second sensor 9770may be used as an optional reference glucose value for the first sensor9760. This effectively provides a reference point as an extra input toserve as a baseline to the calibration-free model. Here, it is importantto emphasize that the arrows indicating the optional reference glucosevalues 9765, 9775 can be uni-directional (i.e., from the first sensor tothe second sensor only, or from the second sensor to the first sensoronly), or bi-directional, as shown in the FIG. 132.

As shown in FIG. 133, in a third embodiment, the first sensor 9780 andthe second sensor 9790 are both calibrated, and they complement eachother. Here, a reference blood glucose (BG) 9782, 9792—which may be thesame BG—is required for each sensor. More specifically, for the purposesof this embodiment, both sensors are calibrated, but the output of eachcalibration model may be used to complement the other sensor's model.This is similar to the embodiment shown in FIG. 132, except that now,both sensors are calibrated. Thus, the output 9785 of the first sensor9780 may be used as an optional reference glucose value for the secondsensor 9790, and/or the output 9795 of the second sensor 9790 may beused as an optional reference glucose value for the first sensor 9780.This effectively provides a reference point as an extra input to serveas a baseline to the calibration model, or can also reduce the totalnumber of reference blood glucose (BG) calibrations needed throughoutthe sensor wear by using a feedback between the two sensors to adjustthe calibration over time.

It bears repeating that the reference glucose value(s) 9782, 9792 forall systems can be the same (or can be different), and, depending on thesystem design, could be an input to a single sensor only, or to bothsensors as shown in FIG. 133. Moreover, as with the embodiment of FIG.132, the arrows indicating the optional reference glucose values 9785,9795 can be uni-directional (i.e., from the first sensor to the secondsensor only, or from the second sensor to the first sensor only), orbi-directional, as shown in the FIG. 133.

In summary, in the embodiment shown in FIG. 133, a reference bloodglucose value is used to start up the sensor system. Calibration factorsare expected to change over time, but the outputs of the other sensorare used to calibrate each sensor over time. For example, the design ofthe first sensor 9780 can be tailored to be more accurate in day 1, andits output can calibrate the second sensor at the beginning of sensorwear. The design of the second sensor 9790 can be tailored to beaccurate later in wear, and its output can be used to calibrate thefirst sensor later in wear. As in the other embodiments, fusion 9730 canbe used to determine the optimal combination dependent on the sensorsystem properties and diagnostics. It is noted that, in this specificembodiment, only 1 (or very few) blood glucose references are neededthroughout the sensor lifetime and, as such, this is an illustrativeexample of a system that is designed to minimize, rather than eliminate,calibrations.

In further embodiments, various combinations of calibrated andnon-calibrated sensors may be used, where a reference blood glucosevalue (and/or an optional blood glucose value) may be required. FIG. 134shows an all-encompassing example in which both calibrated andcalibration-free models may be used in the same system at all times. Inthis illustrative example, a total of four models may be used, whereineach of the two sensors shown may employ a calibrated and anon-calibrated version of the models, which may then be combined. Thus,FIG. 134 shows a first calibrated model 9810, a second calibrated model9820, a first calibration-free model 9830, and a second calibration-freemodel 9840. Here, if one or more reference blood glucose (BG) values9812, 9822 are input into the system, fusion 9730 can temporarily orpermanently place more emphasis on the calibrated model, whereas if noreference blood glucose exists, the calibration-free models could takeover. As noted, any combination of calibration-free and calibratedmodel(s) could exist in this example, and the outputs of all modelscould be used as additional inputs to all other models. It is also notedthat the descriptions hereinabove of the various inputs and outputs thatare shown in FIGS. 129-133 apply equally, where appropriate, for theall-encompassing example shown in FIG. 134. As before, the fusionalgorithm 9730 will determine which combination of SG outputs should beused to compute a final (fused) system sensor glucose value 9735.

While the description above refers to particular embodiments of thepresent invention, it will be understood that many modifications may bemade without departing from the spirit thereof. Additional steps andchanges to the order of the algorithms can be made while stillperforming the key teachings of the present invention. Thus, theaccompanying claims are intended to cover such modifications as wouldfall within the true scope and spirit of the present invention. Thepresently disclosed embodiments are, therefore, to be considered in allrespects as illustrative and not restrictive, the scope of the inventionbeing indicated by the appended claims rather than the foregoingdescription. All changes that come within the meaning of, and range of,equivalency of the claims are intended to be embraced therein.

What is claimed is:
 1. A method for optional external calibration of acalibration-free glucose sensor for measuring the level of glucose in abody of a user, said glucose sensor including physical sensorelectronics, a microcontroller, and a working electrode, the methodcomprising: periodically measuring, by said physical sensor electronics,electrode current (Isig) signals for the working electrode; performing,by said microcontroller, an Electrochemical Impedance Spectroscopy (EIS)procedure to generate EIS-related data for the working electrode; basedon said Isig signals and EIS-related data and a plurality ofcalibration-free SG-predictive models, calculating, by saidmicrocontroller, a respective sensor glucose (SG) value for each of theSG-predictive models; calculating, by said microcontroller, a SGvariance estimate for each respective SG value; determining, by saidmicrocontroller, whether an external blood glucose (BG) value isavailable and, when available, incorporating said BG value into saidcalculation of the SG value; fusing, by said microcontroller, saidrespective SG values from the plurality of SG-predictive models toobtain a single, fused SG value; applying, by said microcontroller, anunscented Kalman filter to said fused SG value; and calculating, by saidmicrocontroller, a calibrated SG value to be displayed to the user. 2.The method of claim 1, wherein the sensor electronics further measurevoltage values of a counter electrode (Vcntr) of said glucose sensor. 3.The method of claim 2, wherein the microcontroller further preprocessessaid Isig signals and Vcntr values prior to calculation of saidrespective SG values.
 4. The method of claim 3, further includingapplying a low-pass filter to said Isig signals.
 5. The method of claim3, wherein said preprocessing comprises down-sampling Isig signals thatare close together in time.
 6. The method of claim 1, wherein saidplurality of SG-predictive models are machine learning models.
 7. Themethod of claim 6, wherein said machine learning models include at leastone of a genetic programming algorithm, a regression decision tree, anda bagged decision tree.
 8. The method of claim 1, wherein said pluralityof SG-predictive models are analytical models.
 9. The method of claim 1,wherein each SG variance estimate for each respective SG value iscalculated empirically from training data.
 10. The method of claim 1,wherein one or more of said respective SG values are modulated for aperiod of time prior to said fusion.
 11. The method of claim 10,wherein, when a BG value is available, said BG value is compared to arespective SG value, and said modulation is performed when a differencebetween said respective SG value and BG value exceeds a threshold. 12.The method of claim 1, wherein said Kalman filter contains one set ofmeasurement functions for when an external BG value is available, andone set of measurement functions for when an external BG value is notavailable.
 13. The method of claim 1, wherein, when an external BG valueis available, said BG value is incorporated into said calculation of theSG value prior to said fusion.
 14. The method of claim 1, wherein, whenan external BG value is available, said BG value is used to adjust saidsingle, fused SG value.
 15. The method of claim 1, wherein the sensorincludes a plurality of working electrodes.